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Math Help - Finding area between curves?

  1. #1
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    Finding area between curves?

    Find the area of the region of
    y= cos x and y=sin2x, x= 0, x=pi/2
    i sketched the curve and y=cos x is on top, so wouldn't it be
    \int cosx-sin2x from pi/2 to 0?
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  2. #2
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    Are you sure that \cos x \geq \sin{2x} on x\in[0,\pi/2]?

    What about x=\pi/4? You need to break up the integral into intervals where one function is greater than or equal to the other.
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  3. #3
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    so would I have to split it into 2 integrals, one where cos x is bigger than sin2x, and the other where sin2x is bigger than cos x?
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  4. #4
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    Yes. In order to do that you need to solve \cos x = \sin{2x}\Leftrightarrow \cos x = 2\cos x \sin x
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