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Quandaries & Queries
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 Topic: integrals
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 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 , JIMAnswered by Robert Dawson. Arclength of an ellipse 2001-07-03 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 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. 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. Riemann sums 2000-03-30 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 dxAnswered by Penny Nom. 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.

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