Recent content by MMM

Homework Statement I'm trying to solve ##\int\sqrt{a^2 - x^2}## by using the substitution ##x = asin\theta## Homework Equations ##x = asin\theta The Attempt at a Solution ##y = \int\sqrt{a^2 - a^2cos^2\theta}## ##y = a\int\cos\theta## ##y = a^2\int\cos(\theta)^2## ##y = (a^2)/2 *...

Thanks for the help. I understand it now!

Homework Statement Hello, I'm having trouble determining what I make u equal with most integrals that revolve around the inverse trig functions. I knew what to let u equal in this problem ##x/\sqrt{1-x^4}## I let it equal ##x^2## and correctly solved the problem. The problems I'm having...

I get it now, I appreciate the help.

Homework Statement I'm curious about how the trapezoidal rule is derived for approximating definite integrals. Homework Equations According to my calculus book the equation is $$h[(1/2)y_{0} + y_{1} + y_{2} + ... +y_{n-1} + (1/2)y_{n}]$$ The Attempt at a Solution I'm curious as to why the...

I split the sum into two different parts. \lim_{n\rightarrow +\infty}\sum_{i=1}^n 8/n and I got that limit to be 8. Now the second sum is \lim_{n\rightarrow +\infty}\sum_{i=1}^n 32i/n^2 and I can't figure out what that limit is. How do I rewrite it as a function of n? Since the final answer...

f(xi) = 2(1 + 4i/n) I edited the first post with that information. I just don't understand why the answer to the problem is 24 and not 8, I have no idea what I did wrong when evaluating the limits. Isn't this \lim_{n\rightarrow +\infty}(4/n) * \sum_{i=1}^\infty\frac{8i}{n} 0? I just don't...

Hello everyone, I've been working on an area summation problem in my book for quite a bit and I can't solve it. Find the area under the straight line y=2x between x = 1 and x = 5 The book shows the answer as 24 and Maple does as well, but I'm not getting 24, I'm getting 8. Area summation formula...