Question

iterated integral

Answer 1

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

Answer 2

So integrate r first.

What is \[\int_0^{cos \theta} r^3 dr\]

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

or could you just uses u substitution?

Answer 11

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

Answer 12

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