Topic: integration list of topics
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	Dividing a region in half		2018-02-24
		From mandy: There is a line through the origin that divides the region bounded by the parabola y=4x−5x2y=4x−5x2 and the x-axis into two regions with equal area. What is the slope of that line? Answered by Penny Nom.
	Integrate (x^2 - 4x + 4) ^4/3		2016-09-15
		From Ifah: Hi i have questions please answer Integral 2 sampai 3 dari (x² - 4x + 4) ^4/3 dx Answered by Penny Nom.
	The integral of a sum		2016-03-10
		From Rahul: How to solve definite integral of a sum. The specific problem is as follows, Integral of ( 1+ sum of x^k, k=1 to k=n), x=0 to x=b *dx. The answer is b + sum of b^(k)/k, k=2, to k=n+1. I understand only the integral of first term. But integral of the sum I do not understand at all. Answered by Penny Nom.
	Integration of dx/(x^2+1)^3		2016-01-07
		From Ishank: Integration of dx/(x^2+1)^3 Answered by Penny Nom.
	The area bounded by the X-axis and y=x^(2)-4 from -5 to 0		2014-04-15
		From Lexie: Determine the area that is bounded by the following curve and the x-axis on the interval below. (Round your answer to three decimal places) y=x^(2)-4, -5 ≤ x ≤ 0 The answer is 32.333 but I have no idea how to get there. Answered by Penny Nom.
	Integration from 0 to 2pi of 1/(3cos x + 2) dx		2013-02-04
		From ankit: Integration from 0 to 2pi of 1/(3cos x + 2) dx Answered by Harley Weston.
	An integral		2012-12-16
		From Slavena: integration of (lnx)^2 / x dx Answered by Penny Nom.
	Integral 1/(25-x^2)^3/2		2012-02-22
		From John: Integral 1/(25-x^2)^3/2 Answered by Harley Weston.
	A volume of revolution		2012-01-11
		From john: find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the x-axis about the line y=8. The answer in the back of the book is 704 pi divided by5 Answered by Penny Nom.
	An antiderivative of the square root of (8t + 3)		2011-04-19
		From Caitlyn: I know how to take an antiderivative. But this one's stumping me. I need it to finish a problem. What's the antiderivative of the square root of (8t + 3) ~Caitlyn= Answered by Penny Nom.
	Integrating ln^3x/x		2011-01-14
		From ken: y=ln^3x/x from x=1 to x=11 Answered by Penny Nom.
	The integral of (x^2*exp(x)/(exp(x)-1)^2		2010-08-09
		From sujoy: please find this integral for me int(x^2*exp(x)/(exp(x)-1)^2 Answered by Robert Dawson.
	Integration of sin^3 (2x)		2010-05-29
		From ascher: how do you integrate this equation ∫ sin^3 (2x) dx Answered by Robert Dawson and Penny Nom.
	Integrate the ((4th root of x^3)+1) dx		2010-04-12
		From Bridget: integrate the ((4th root of x^3)+1) dx Answered by Tyler Wood.
	The integral of X^3/the square root of 1-x^2 dx		2010-03-07
		From William: The integral of X^3/the square root of 1-x^2 dx. Answered by Harley Weston.
	Integration of cos (x^2+y^2) dx dy		2010-02-12
		From anna: How do you evaluate the integration of integration of cos (x^2+y^2) dx dy? Answered by Tyler Wood.
	An integral		2010-01-29
		From amr: find the value of the following integral:- (1+x)power (-1/2) dx Answered by Robert Dawson.
	The integral of sqrt(x) * ln(x)		2009-10-12
		From Oana: Hi! Can you tell me please how much is : ∫ (√x * ln x) ? Answered by Penny Nom.
	Integration of cos (x^2) dx		2009-10-12
		From Venkat: How do you evaluate the integration of cos (x^2) dx ? Answered by Harley Weston.
	solve integral of ( x^2+x+1)^5		2009-09-18
		From jaka: solve integral of ( x^2+x+1)^5 Answered by Robert Dawson.
	An antiderivative problem		2009-08-13
		From Indrajit: ∫4e^x + 6e^-x/(9e^x + 4e^-x)dx = Ax + Bloge(9e2x - 4) + C then A=?......B=?.....C=? plz solve it...."^" stands for "to the power of".... Answered by Harley Weston.
	The integral of x^x		2009-06-18
		From ANGIKAR: what would be the integration of (X^Xdx)? give answer in details. Answered by Robert Dawson and Harley Weston.
	The integral of a to power x squared		2009-04-28
		From JIM: WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE SOLVED : a to power x squared . is this still true ? CURIOUS , JIM Answered by Robert Dawson.
	The integral of the square root of the sine function		2009-04-07
		From Indrajit: how to integrate this derivative??? ∫√sinx Answered by Harley Weston.
	The area between the x-axis and a curve		2009-02-18
		From Lauren: This is from a homework question I can't figure out. Let R be the region in the fourth quadrant enclosed by the x-axis and the curve y= x^2 - 2kx, where k > 0. If the area of the region R is 36 then what is the value of k? Answered by Robert Dawson.
	The integral of f(x)dx and the integral of f(x-4)dx		2009-01-02
		From Katie: Calculus: If the definite integral from -2 to 6 of f(x)dx=10 and the definite integral from 2 to 6 of f(x)dx=3, then the definite integral from 2 to 6 of f(x-4)dx= ? I don't understand how to solve definite integrals when the function has something more than just x inside the parenthesis such as f(4-x). Answered by Robert Dawson.
	Antiderivative of 1/(x(1 - x))		2008-10-22
		From Matt: derivative of dx/(x(1-x)) From what I've seen I should break apart the equation as such derivative of dx/x - dx/(1-x) and then get the 2 corresponding log functions. If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative. Answered by Harley Weston.
	Integration		2008-10-17
		From hazela: integration of x sinx cosnx Answered by Harley Weston.
	Integral of X^2		2008-07-28
		From Hemanshu: Integral of X^2 Answered by Janice Cotcher.
	The volume of a solid		2008-06-04
		From Tom: The base of a certain solid is a circle of radius 2 while cross sections perpendicular to the base are isosceles triangles of height 1. What is the volume of the solid? Answered by Harley Weston.
	The weight of a concrete column		2008-05-11
		From russell: a cylindrical form is filled with a slow curing concrete. The base of the form is 10 ft in radius, and height is 25 ft. while the concrete hardens, gravity causes the density to vary from a density of 90 lbs/ft^3 at the bottom to a density of 50 lb/ft^3 at the top. Assume that the density varies linearly from the top to the bottom, and compute the total weight of the resulting concrete column Answered by Harley Weston.
	Integrate 2x(x^2-1)^5 dx		2008-04-17
		From joey: pls help me to integrate 2x(x^2-1)^5 dx using the substitution u=x^2-1 Answered by Harley Weston.
	The integral of dx / (4x^2 - 25)^3/2		2008-04-01
		From Meghan: I have a question from the trigonometric substitution of my calculus course. integral of dx / (4x^2 - 25)^3/2 Answered by Harley Weston.
	Integrate (4+x^2) / (x (2+x)^2)		2008-02-25
		From Russell: integrate (4+x^2) / (x (2+x)^2) I really need to know the steps involved in doing this integral, I already have the answer through wolfram integrator but for some reason can not get to the answer given. Please help Answered by Harley Weston.
	Two regions with equal area		2008-02-13
		From James: There is a line through the origin that divides the region bounded by the parabola y=3x-5x^2 and the x-axis into two regions with equal area. What is the slope of that line? Answered by Harley Weston.
	Integration by parts		2008-01-30
		From seth: hi i really dont understand integr ation by parts. for example, the integral(t^2sintdt. i have u=t^2 and v'=sint also u'=t^/3 v=-cost for the formula i have uv-integralvu' dx this is all well and good but i cant get it right. Answered by Harley Weston.
	The integral of Sqrt(sin x)		2008-01-24
		From tariq: find integration Sqrt(sinx) dx , from x=bi/4 to 3bi/4 Answered by Harley Weston.
	An integral		2008-01-24
		From Meghan: Evaluate the indefinite integral of (x^3 +1)^(1/3) * x^5 * dx. Answered by Brennan Yaremko.
	Integration		2008-01-23
		From Russell: how to integrate 1/x ln^2 [x] dx Answered by Harley Weston.
	Two integrals		2007-11-09
		From Akilan: how to integrate these (tan x)^6(sec x)^4 and sinh(x)(cosh(x))^2. Please send me how to do this question. Having exams on Monday. Please help. Answered by Harley Weston.
	Integration		2007-02-02
		From Jenna: How do I integrate ( ln(x) ) / ( x^2 ) ? Answered by Penny Nom and Claude Tardif.
	The volume of a frustum of a pyramid		2007-01-17
		From Sam: Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h. Answered by Penny Nom.
	Integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4		2007-01-09
		From James: How do you integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 Answered by Penny Nom.
	An Integral		2006-07-30
		From Aniket: I am Aniket studing in 12 th standard At Mumbai I have following integration problem please give me a solution integral of 1/under root of (5x2 - 2x) dx Answered by Penny Nom.
	The integral of tan^4x		2005-03-31
		From Nicole: college student. need help with tough integral. the integral of 2tan4xdx Answered by Penny Nom.
	Approximating an integral		2005-01-27
		From A student: i used excel to find the area under a graph instead of integrating the function the analytical way. These are the different answers i got with different width of the x-values, the smaller the x-increment gets the more precise the area is when compared to the answer obtained the numerical way. I have trouble seeing why the answers i get is getting bigger and bigger and not smaller can someone plz explain? Answered by Penny Nom.
	Integrating e^sin(x)		2004-08-04
		From A student: I need to know that how to solve the integral " e^sin x", Answered by Harley Weston.
	A helicopter rises vertically		2003-09-02
		From Kate: A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)2 How far above the ground will the helicopter be after 3 seconds? Answered by Penny Nom.
	Odd powers of sine and cosine		2003-06-25
		From Antonio: Can you please tell me how to integrate a trig function involving sine and cosine? I know if the powers of both the sine and cosine are even and nonnegative, then I can make repeated use of the power-reducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx. Answered by Harley Weston.
	Integrating e^x sin(x)		2003-05-03
		From Lech: I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer. Answered by Penny Nom and Claude Tardif.
	Integration of 1/(2+cos(x))		2003-01-07
		From A student: integral from pi to 0 of dx/(2+cos x) i used the substitution t=tan(x/2) and i ended up with integral from +infinity to 0 of 2dt/(t2+3) which looks like an inverse tan function , and i ended up with sqr(27)/2 pi , which is not the same as my calculator's answer , so i suspct i am doing some thing wrong. can some one tell me where i am going wrong please. Answered by Penny Nom.
	Integrating x^x		2002-06-18
		From Jeremy: I am a student at the University of Kansas and I am wondering if there is a general anti-derivative for x x (i.e. the integral of x x dx)? I've looked in a bunch of Table of Integrals and have found nothing (can you guys find it?), so I'm sort of wondering if this may be a research type question. Answered by Claude Tardif.
	Arc length		2002-04-17
		From Vix: Find the point on the curve r(t)=(12sint)i-(12cost)j+5tk at a distance 13pi units along the curve from the point (0,-12,0) when t=0 in the direction opposite to the direction of increasing arc length. Answered by Harley Weston.
	The probability that the area of a triangle is smaller that 1/8		2001-12-21
		From Hoda: Given unit square pick two points on adjacent sides of the square , what is the probability that the area of the resulting triangle is smaller that 1/8? I tried to tackle the problem by first sketching a square with the four vertices at (0,0), (1,1), (0,1) and (1,1). The answer seems to be the area under the curve y=0.25/x between 1 and 0, but how can you integrate such a function when ln0 is undefined? any help would be highly appreciated. Answered by Andrei Volodin.
	Area between curves		2001-06-13
		From Phil: question 1 find the area bound by the curves y = x2 + 2x + 3 and y = 2x + 4 question 2 Find the volume generated by rotating the curve x2 + y2 = 9 about the x-axis Answered by Harley Weston.
	National consumption function		2001-05-09
		From Brian: If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function. Answered by Harley Weston.
	The average value of a continuous function		2001-05-08
		From Esther: The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Answered by Harley Weston.
	Oil revenue		2001-04-21
		From Brian: Suppose that t months from now an oil well will be producing crude oil at the rate of r(t), not a constant, barrels per month and that the price of crude oil will be p(t), not a constant, dollars per barrel. Assume that the oil is sold as soon as it is extracted from the ground. Find an expression for the total revenue from the oil well, R(t). A certain oil well that currently yields 400 barrels of crude oil a month will run dry in 2 years. The price of crude oil is currently $18 per barrel and is expected to rise at a constant rate of 3 cents per barrel per month. What will be the total revenue from this well? {Hint: Model the degraded production rate with the equation: r(t) = (A-Bt)e0.04t} Answered by Harley Weston.
	Integration by parts		2001-04-09
		From A student: how do you integrate x tan-1x dx, i know it can be done by integration by parts maybe, but i'm not sure.... Answered by Claude Tardif and Harley Weston.
	Two integrals		2001-04-03
		From Jim: I'm having trouble with these integrals. Can you help me out? 1)the integral of: x5 arctan x dx 2)the integral of: 2x5 + 9x4 + 19x3 + 13x2 - 5x - 25 ----------------------------------------------- dx x4 + 4x3 + 5x2 Answered by Claude Tardif.
	A jogger		2001-03-12
		From Bill: At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes. a) write an expression for the velocity of the jogger at time t. b) what is the total distance traveled by the jogger in that 10-minute interval. Answered by Harley Weston.
	How do you integrate secant(theta)?		2000-12-22
		From Robert Williamson: How do you integrate secant(theta)? I know the answer is ln [sec(theta) + tan(theta)] but how do you get there? Answered by Claude tardif.
	A non-integrable function		2000-12-03
		From Mark Spilker: I have a proof that I cannot do here it goes. Let F(x)= 1 if x is a rational number 0 if x is an irrational number Prove the function is not intregrable on the interval (0,1). Hint: Show that no matter how small the norm of the partition, the Riemann Sum for the SigmaNotation F(wi) DeltaiX is not unique. Answered by Harley Weston.
	An integration problem		2000-11-30
		From A student: If a>0 and the integral from b to 0 of 1/(1+x) equals 1/2 the integral from a to 0 of 1/(1+x), express "b" in terms of "a" Answered by Claude tardif.
	Comparing an integral and a sum		2000-11-21
		From Douglas Norberg: A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 230 which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum. When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2x from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Answered by Harley Weston.
	Dividing a region in half		2000-09-21
		From Kerry: There is a line through the origin that divides the region bounded by the parabola y=x-x2 and the x-axis into two regions with equal area. What is the slope of the line? Answered by Penny Nom.
	Calculus Research Questions		2000-05-22
		From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston.
	Two calculus problems		2000-05-01
		From Kaushal Shah: How Do WE Integrate the following Functions, Integral xtanx dx How was natural base "e" discovered and why e=2.7....... Answered by Claude Tardif.
	The area of a triangle using calculus		2000-04-15
		From Todd Bowie: Hi, I am not a student but am reviewing calculus for an upcoming interview. I would like to know how to derive the area of a triangle using calculus. Thanks! Answered by Patrick Maidorn.
	Some integration problems		2000-02-23
		From Tim Valentine: I am having a great deal of difficulty with the following integrals, can you help? I think they need the use of trig substitution or integration by parts but I cannot figure out how to begin. Thanks! The integral of 1/(2+3x2) dx. and The integral of x * square root of (4x+5) dx. Answered by Harley Weston.
	Two calculus problems		1999-12-13
		From Alan: I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks. Question 1: A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2 Question 2: How many trapezoids must one use in order for the error to be less than 10^-8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found. Answered by Harley Weston.
	The area and the circumference of a circle.		1998-08-27
		From Jason Wright: I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me! Answered by Walter Whiteley.
	Calculus problems		1998-07-13
		From Lorraine: I'm stuck again. Can you help? This involves integration using the method of partial fractions the integral of: 7x(to the 5th) - 2x(cubed) + 3 dx -------------------------------------- x(to the fourth) - 81 Do I have to do long division to reduce the numerator to the fourth power? the integral of: 4- 16x +21x(squared) + 6x(cubed) - 3x(fourth) dx ---------------------------------------------------- x(cubed)(x - 2)(squared) Lorraine Answered by Harley Weston.
	A Calculus Problem		1998-06-28
		From Lorraine: I'm a post-secondary student taking calculus by correspondence. I'm stuck on the following question (and similar ones) Can you help? Evaluate the following indefinite integral: d(theta) ---------- 1 + sin (theta) (It says to multiply both numerator and denominator by: 1 - sin(theta) Thanks Lorraine Answered by Harley Weston.

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