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Math Help - Polar Double Integration help

  1. #1
    Member FalconPUNCH!'s Avatar
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    Polar Double Integration help

    I'm doing polar integration and I'm having some problems.

    4*\int_{0}^{\frac{\pi}{2}} \int_{0}^{1} ln(r^{2}+1)rdrd\theta

    The answer comes out to

    \pi(ln(4)-1) but I always end up with \pi(ln(2)-1)
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by FalconPUNCH! View Post
    I'm doing polar integration and I'm having some problems.

    4*\int_{0}^{\frac{\pi}{2}} \int_{0}^{1} ln(r^{2}+1)rdrd\theta

    The answer comes out to

    \pi(ln(4)-1) but I always end up with \pi(ln(2)-1)
    If you show your working it will be easier to see your mistake.

    The only 'hard' bit is finding \int_{1}^{2} \ln u \, du = 2 \ln (2) - 1 where u = r^2 + 1. Note the integrals terminals (this is probably what you forgot).
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  3. #3
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by mr fantastic View Post
    If you show your working it will be easier to see your mistake.

    The only 'hard' bit is finding \int_{1}^{2} \ln u \, du = 2 \ln (2) - 1 where u = r^2 + 1. Note the integrals terminals (this is probably what you forgot).
    I would have shown my work but it's two pages long and messy. I think it's because I didn't try substituting. I'll try that thanks.
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