Why Does Reversing Limits of Integration Affect the Answer?

[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?

 

[Mark44]

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?

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

 

[Miike012]

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

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

 

[Mark44]

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

 

[Miike012]

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

So it is correct to integrate from pi to 0?

 

[Mark44]

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.