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tdabboud

  • 3 years ago

iterated integral

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  1. tdabboud
    • 3 years ago
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    \[\int\limits_{0}^{\pi/2} \int\limits_{0}^{\cos \theta} r^3 drd \theta\]

  2. polpak
    • 3 years ago
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    So integrate r first. What is \[\int_0^{cos \theta} r^3 dr\]

  3. tdabboud
    • 3 years ago
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    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
    • 3 years ago
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    taking the integral of that before evaluating seems to be some long number however

  5. chaguanas
    • 3 years ago
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    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
    • 3 years ago
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    It should be just \[\int_0^{\pi/2}[\frac{1}{4}cos^4\theta ]d\theta\]

  7. polpak
    • 3 years ago
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    Evaluating \[\frac{r^4}{4}\] at r=0 does not give you 1/4

  8. tdabboud
    • 3 years ago
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    wow I am dumb, I was evaluating the cos again, okay you were right with the last statement

  9. polpak
    • 3 years ago
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    And for integrating cos^4 I think you need to make use of the half angle formula.

  10. tdabboud
    • 3 years ago
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    or could you just uses u substitution?

  11. polpak
    • 3 years ago
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    You can try, but I don't think it'll work out as nicely.

  12. tdabboud
    • 3 years ago
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    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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