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Math Help - Finding I(x)

  1. #1
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    Finding I(x)

    Okay so the question goes

    For x in [-pi/2,pi/2], define  I(x)=\int_{sin(x)}^{cos(x)}\frac {1} {t+(\sqrt(1-t^2))} dt

    Find I(x) by showing that dI/dx = -1 and that I(pi/4)=0.

    I have the done the first part, ie showing that dI/dx= -1 and that I(pi/4)=0. However, I can't figure out how to use my answer to that part to find I(x). Can anyone help?
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  2. #2
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    Quote Originally Posted by nmatthies1 View Post
    Okay so the question goes

    For x in [-pi/2,pi/2], define  I(x)=\int_{sin(x)}^{cos(x)}\frac {1} {t+(\sqrt(1-t^2))} dt

    Find I(x) by showing that dI/dx = -1 and that I(pi/4)=0.

    I have the done the first part, ie showing that dI/dx= -1 and that I(pi/4)=0. However, I can't figure out how to use my answer to that part to find I(x). Can anyone help?
    looks like you did all the hard work ...

    \frac{dI}{dx} = -1

    I(x) = -x + C

    I \left(\frac{\pi}{4}\right) = 0

    I(x) = \frac{\pi}{4} - x
    Last edited by skeeter; February 14th 2009 at 01:37 PM. Reason: fixed my dyslexic initial condition
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  3. #3
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    Oh yes of course! I was looking for something harder I guess. Thanks!
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