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Math Help - Calculus Problems

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    Calculus Problems

    Find the area of the region bounded by the curves y=1/x, y=x, y=x/4 where x>0 .
    Last edited by mr fantastic; November 28th 2008 at 07:47 PM. Reason: Clarification given by OP
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  2. #2
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    Quote Originally Posted by Nimmy View Post
    Find the area of the region y=1/x, y=x, y=x/4 x>0 .
    Have you drawn the graphs of each curve and hence shaded the required region? This is absolutely essential.

    Then you should see that the area is given by

    A = \int_0^1 x - \frac{x}{4} \, dx + \int_1^2 \frac{1}{x} - \frac{x}{4} \, dx.

    The integral terminals come from considering the intersection points of y = \frac{1}{x} with y = x and y = \frac{x}{4}.
    Last edited by mr fantastic; November 28th 2008 at 07:47 PM. Reason: Whoops. Didn't see the x > 0.
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