







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. 





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. 





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. 





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.


