Posted by **Dora** on Friday, July 3, 2009 at 9:16pm.

evaluate the following integrals by any means possible:

b. integral from -1 to 1 (w/ (w^2+1)) (dw)

c. integral from -3 to 0 sqrt(9-x^2)dx

- calculus -
**Count Iblis**, Friday, July 3, 2009 at 9:30pm
b) zero because the function is odd.

c) substitute x = 3 sin(t)

Integral from -pi/2 to 0 of

9 cos^2(t) dt

If you were to replace cos^2 by sin^2 in this integral, the answer would be the same because

cos(x) = -sin(-pi/2-x) ------->

cos^2(x) = sin^(-pi/2 - x)

So, the values attained by cos^2 are also attained by sin^2 in the inteval from -pi/2 to 0. If we call the integral I, then:

2 I = 9 Integral of

[cos^2(t) + sin^2(t)] dt from -pi/2 to 0 =

9* pi/2 --------->

I = 9/4 pi

## Answer this Question

## Related Questions

- Calculus - Find the volume of the solid whose base is the region in the xy-plane...
- Calculus - Integrals - I have 3 questions, and I cannot find method that ...
- Calculus - Integrals - I have 3 questions, and I cannot find method that ...
- Calc 2 - a. Integral (x^2)/(sqrt(1+(x^2))) Would I separate these two into 2 ...
- Calculus II - Evaluate using u-substitution: Integral of: 4x(tan(x^2))dx ...
- Calculus integral - evaluate the integral: integral from -pi/4 to 0 for the ...
- ap calculus - Which of the following definite integrals gives the length of y = ...
- CALCULUS 2!!! PLEASE HELP!! - I'm having trouble with this question on arc ...
- calc II - Express the integrals as the sum of partial fractions and evaluate the...
- calculus - There are four integrals: 1) definite integral x/(1+x^4)dx b/w ...