anonymous
  • anonymous
iterated integral
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{0}^{\pi/2} \int\limits_{0}^{\cos \theta} r^3 drd \theta\]
anonymous
  • anonymous
So integrate r first. What is \[\int_0^{cos \theta} r^3 dr\]
anonymous
  • anonymous
Thats the thing I am getting stuck right after that so I have this: \[\int\limits_{0}^{\pi/2}[[\cos \theta]^4/4 - 1/4] d \theta\]

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anonymous
  • anonymous
taking the integral of that before evaluating seems to be some long number however
anonymous
  • 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
anonymous
  • anonymous
It should be just \[\int_0^{\pi/2}[\frac{1}{4}cos^4\theta ]d\theta\]
anonymous
  • anonymous
Evaluating \[\frac{r^4}{4}\] at r=0 does not give you 1/4
anonymous
  • anonymous
wow I am dumb, I was evaluating the cos again, okay you were right with the last statement
anonymous
  • anonymous
And for integrating cos^4 I think you need to make use of the half angle formula.
anonymous
  • anonymous
or could you just uses u substitution?
anonymous
  • anonymous
You can try, but I don't think it'll work out as nicely.
anonymous
  • anonymous
okay well thanks for your help atleast I got passed that one error I should be able to get it from here

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