Homework Help: Limits of integration

1. Dec 9, 2012

Miike012

My limits of integration for my angle I chose to be from pi to 0 then I got the negative answer from what was in the book.. Shouldn't that be correct because we are integrating from -3 to 3?

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2. Dec 10, 2012

Staff: Mentor

What did you get for your answer? I got a positive value for the integral, a tad over 3.

3. Dec 10, 2012

Miike012

when I integrated from pi to 0 I got 1/2pi(cos(9) - 1)

4. Dec 10, 2012

Staff: Mentor

That should be -(1/2)pi *(cos(9) - 1). The antiderivative of sin(u) is -cos(u).

5. Dec 10, 2012

Miike012

So it is correct to integrate from pi to 0?

6. Dec 10, 2012

Staff: Mentor

It's correct to integrate from 0 to pi, like so:
$$\int_{\theta = 0}^{\pi} \int_{r = 0}^3 sin(r^2)r~dr~d\theta$$

Is that what you meant? If you meant $\pi$ as the lower limit of integration, and 0 as the upper limit, you'll get the opposite value.