## anonymous 5 years ago iterated integral

1. anonymous

$\int\limits_{0}^{\pi/2} \int\limits_{0}^{\cos \theta} r^3 drd \theta$

2. anonymous

So integrate r first. What is $\int_0^{cos \theta} r^3 dr$

3. anonymous

Thats the thing I am getting stuck right after that so I have this: $\int\limits_{0}^{\pi/2}[[\cos \theta]^4/4 - 1/4] d \theta$

4. anonymous

taking the integral of that before evaluating seems to be some long number however

5. anonymous

I think you need a little more work. cos theta shouldn't be an end point. As part of the set up you should evaluate cos theta and come up with some number for example cos pi/4 is square root 2

6. anonymous

It should be just $\int_0^{\pi/2}[\frac{1}{4}cos^4\theta ]d\theta$

7. anonymous

Evaluating $\frac{r^4}{4}$ at r=0 does not give you 1/4

8. anonymous

wow I am dumb, I was evaluating the cos again, okay you were right with the last statement

9. anonymous

And for integrating cos^4 I think you need to make use of the half angle formula.

10. anonymous

or could you just uses u substitution?

11. anonymous

You can try, but I don't think it'll work out as nicely.

12. anonymous

okay well thanks for your help atleast I got passed that one error I should be able to get it from here