## tdabboud 4 years ago iterated integral

1. tdabboud

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

2. polpak

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

3. tdabboud

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. tdabboud

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

5. chaguanas

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. polpak

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

7. polpak

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

8. tdabboud

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

9. polpak

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

10. tdabboud

or could you just uses u substitution?

11. polpak

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

12. tdabboud

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