







The derivative of x! 
20160416 

From Sang: How to find the derivative of x! and integral of x! Answered by Penny Nom. 





The integral of a sum 
20160310 

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 
20160107 

From Ishank: Integration of dx/(x^2+1)^3 Answered by Penny Nom. 





The area bounded by the Xaxis and y=x^(2)4 from 5 to 0 
20140415 

From Lexie: Determine the area that is bounded by the following curve and the xaxis 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 
20130204 

From ankit: Integration from 0 to 2pi of 1/(3cos x + 2) dx Answered by Harley Weston. 





An integral 
20121216 

From Slavena: integration of (lnx)^2 / x dx Answered by Penny Nom. 





Integral 1/(25x^2)^3/2 
20120222 

From John: Integral 1/(25x^2)^3/2 Answered by Harley Weston. 





Integrating ln^3x/x 
20110114 

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 
20100809 

From sujoy: please find this integral for me
int(x^2*exp(x)/(exp(x)1)^2 Answered by Robert Dawson. 





The integral of X^3/the square root of 1x^2 dx 
20100307 

From William: The integral of X^3/the square root of 1x^2 dx. Answered by Harley Weston. 





Integration of cos (x^2+y^2) dx dy 
20100212 

From anna: How do you evaluate the integration of integration of cos (x^2+y^2) dx dy? Answered by Tyler Wood. 





An integral 
20100129 

From amr: find the value of the following integral:
(1+x)power (1/2) dx Answered by Robert Dawson. 





Integration of cos (x^2) dx 
20091012 

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 
20090918 

From jaka: solve integral of ( x^2+x+1)^5 Answered by Robert Dawson. 





A sundial on an elliptical cylinder 
20090722 

From Leo: I want to build a sundial where the shadow falls on an elliptical cylinder. I can
calculate the coordinates of the points on the cylinder that I want to mark.
My problem is that I will have to make the surface as a flat sheet and bend it
into an elliptical shape. However, I cannot work out a scheme to transfer
the coordinates I know into a distance that will work when I bend the shape.
Help! Answered by Robert Dawson. 





Area under curve 
20090721 

From Morag: What is the area bounded by the curve y=X^2(2X) and the x axis between x=0 and x=2? Answered by Janice Cotcher. 





The integral of a to power x squared 
20090428 

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. 





A definite integral 
20090209 

From Mathata: Evaluate: integral from 0 to 1, x^2 e^x^3dx Answered by Harley Weston. 





An integral from 1 to infinity 
20090124 

From Ray: Determine the area bounded by the xaxis and the curve y=1/(x^2) from x=1 to x=infinity.
A. 1.00
B. infinity
C. indeterminate
D. 2.00 Answered by Harley Weston. 





The integral of f(x)dx and the integral of f(x4)dx 
20090102 

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(x4)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(4x). Answered by Robert Dawson. 





Integral of cos^2 X between pi/2 and 0 
20081218 

From Wanda: Integral or Area of cos^2 X between pi/2 and 0.
The answer that I got is pi/4. Is this correct? If not, how did you come up with your answer? Answered by Robert Dawson. 





Antiderivative of 1/(x(1  x)) 
20081022 

From Matt: derivative of dx/(x(1x))
From what I've seen I should break apart the equation as such
derivative of dx/x  dx/(1x)
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. 





A dog tied to a round building 
20080708 

From maitham: i have this question which i don't know how to solve it :
One dog was linked to the outer wall of a building round of 20 meters in diameter. If the length of chain linking the dog sufficient turnover of half the distance around the building,
What area can guard dog?
they said that we can solve it by integral .. can you solve it for me? Answered by Harley Weston. 





What is the integral of 13sin^3(x)*cos^7(x)dx? 
20080422 

From Cathrine: I am having trouble integrating this problem. It says to evaluate the integral but I don't know what to do or how to do it.
It is the integral of
13sin^3(x)*cos^7(x)d Answered by Harley Weston. 





Integrate 2x(x^21)^5 dx 
20080417 

From joey: pls help me to integrate
2x(x^21)^5 dx using the substitution u=x^21 Answered by Harley Weston. 





The integral of dx / (4x^2  25)^3/2 
20080401 

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. 





An integral 
20080124 

From Meghan: Evaluate the indefinite integral of (x^3 +1)^(1/3) * x^5 * dx. Answered by Brennan Yaremko. 





An integral 
20080123 

From Russell: I checked out the integration site, but would like an explanation for integrating this integral
Tan^3[x] * _dx__
Cos^2[x]
Hope this input is correct!
the part that throws me off is Tan^3[x], if it was squared rather than cubed I would have a easier time
dealing with this one. Answered by Harley Weston. 





The integral of 1/ (x(x+1)^0.5) 
20071229 

From Nooruddin: Integral of
dx / x(x+1)^0.5
(boundaries are 5 and 3) Answered by Harley Weston. 





Can't find circumference of an ellipse 
20070706 

From Michele: I need to figure the circumference of an oval and I know the height and width. Answered by Penny Nom. 





Using calculus to prove the formula for the area of a triangle 
20070704 

From Apratim: Using calculus how can one show that the area of any triangle is 1/2 times its base times its height? Answered by Stephen La Rocque. 





Integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 
20070109 

From James: How do you integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 Answered by Penny Nom. 





An Integral 
20060730 

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 (5x^{2}  2x) dx
Answered by Penny Nom. 





integral of tan^4 x 
20060514 

From Aqil: integral of tan^{4} x Answered by Penny Nom. 





The integral of tan^4x 
20050331 

From Nicole: college student. need help with tough integral.
the integral of 2tan^{4}xdx
Answered by Penny Nom. 





Integration of 1/(2+cos(x)) 
20030107 

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/(t^{2}+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. 





Arclength of an ellipse 
20010703 

From A hobbyist: What is the equation (with the length of the arc as a variable) for one quadrant of the ellipse,... Answered by Claude tardif. 





The average value of a continuous function 
20010508 

From Esther: The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Answered by Harley Weston. 





Two integrals 
20010403 

From Jim: I'm having trouble with these integrals. Can you help me out? 1)the integral of:
x^{5} arctan x dx 2)the integral of:
2x^{5} + 9x^{4} + 19x^{3} + 13x^{2}  5x  25  dx x^{4} + 4x^{3} + 5x^{2} Answered by Claude Tardif. 





Comparing an integral and a sum 
20001121 

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 * 2^{30} 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 * 2^{x} from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Answered by Harley Weston. 





Integral solutions 
20001120 

From David: determine all pairs of integers (x,y) which satisfy the equation 6x^{2}  3xy  13x + 5y = 11 I got y= (6x^{2}13x+11)/(3x5) and i don't konw how to continue Answered by Claude Tardif. 





An improper integral 
20000504 

From A high school senior: Hi, I am a high school senior and I need help stugying for a final. I am stuck on one of the questions on my review sheet. Does the improper integral from 5 to infinity of (38/97)^{x} converge or diverge? If it converges I also need to know how to find the approximate value accurate to .01 of its actual value. Answered by Harley Weston. 





An indefinite integral 
20000503 

From Bonnie Null: I am to find the indefinite integral of: (e^{x}  e^{x})^{2} dx Answered by Claude Tardif. 





Riemann sums 
20000330 

From Joshua D. Parham: If n is a positive integer, then
lim (1/n)[1/(1+1/n) + 1/(1+(2/n) + ... + 1/(1+n/n)]
n>infinity
can be expressed as the integral from 1 to 2 of 1/x dx Answered by Penny Nom. 





Two calculus problems 
19991213 

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 average rate of change of a function 
19990420 

From Tammy: Suppose that the average rate of change of a function f over the interval from x=3 to x=3+h is given by 5e^h4cos(2h). what is f'(3)? I would appreciate any help with this question. Answered by Harley Weston. 

