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Math Help - shaded region

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    shaded region

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  2. #2
    Super Member Aryth's Avatar
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    Well, we know that:

    \left|\int_a^b [f(x)]dx\right| = Area

    Well, we know the following:

    a = 1 We know this because the -1 at the end shifts it to the right 1.

    b = 4 It is labeled as the end of the region.

    y = f(x) = \frac{1}{x^2} - 1

    So, therefore:

    \left|\int_1^4 [\frac{1}{x^2} - 1]dx\right|

    So now we have to rewrite it in a way that would make this easier to integrate:

    \left|\int_1^4 [x^{-2} - 1]dx\right|

    Now we integrate:

    |[-x^{-1} - x]_1^4|

    \left|\left[\left(-\frac{1}{4} - 4\right) - (-1 - 1)\right]\right|

    \left|\left[\left(-\frac{5}{4}\right) + 2\right]\right|

    \left|\frac{3}{4}\right| \text{units}^2 = \frac{3}{4} \text{units}^2 = Area

    There you go.
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