## tdabboud Group Title iterated integral 3 years ago 3 years ago

1. tdabboud Group Title

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

2. polpak Group Title

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

3. tdabboud Group Title

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 Group Title

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

5. chaguanas Group Title

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 Group Title

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

7. polpak Group Title

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

8. tdabboud Group Title

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

9. polpak Group Title

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

10. tdabboud Group Title

or could you just uses u substitution?

11. polpak Group Title

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

12. tdabboud Group Title

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