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Math Help - How do I find area between functions using integrals if...?

  1. #1
    s3a
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    How do I find area between functions using integrals if...?

    How do I find area between functions using integrals if there are more than two functions as shown in the attached pdf as #15?

    Any input would be greatly appreciated!
    Thanks in advance!

    P.S.
    The functions are y = 1/x, y = x, y = x/4, x >0. You don't really need to count x>0 since the restriction is within the other three functions assuming I sketched it correctly (as shown in the pdf file).
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  2. #2
    Member Black's Avatar
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    Your points of intersection will be (1,1) and (2, 1/2). Split the area into two parts: the part of the area left and the part right of the line x=1 . On the left, your 'top' function will be y=x and your 'bottom' function will be y=x/4. On the right, y=1/x is the top and y=x/4 is the bottom. Therefore, your area will be

    A=\int_{0}^{1}\left(x-\frac{x}{4}\right)dx+\int_{1}^{2}\left(\frac{1}{x}-\frac{x}{4}\right)dx.
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