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Math Help - Find the area of the finite region

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    Find the area of the finite region

    Find the area of the finite region bounded by the curve with equation x^2 - y^2 = 4 and the line x = 5.

    So to find the region we've to find, int (x^2 - 4)^1/2 dx with limit 0-5. But how do I integrate this?
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by geton View Post
    Find the area of the finite region bounded by the curve with equation x^2 - y^2 = 4 and the line x = 5.

    So to find the region we've to find, int (x^2 - 4)^1/2 dx with limit 0-5. But how do I integrate this?
    You will need to apply a trigonometric substitution to the integral, in particular, the substitution x=2sec(\theta). Differentiating x, we get dx=2sec(\theta)tan(\theta)d\theta. For now, don't worry about the limits of integration. The integral will become the following:
    \int\sqrt{4sec^2(\theta)-4}*2sec(\theta)tan(\theta)d\theta

    Take it from there, and see how you go.
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