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Math Help - integral

  1. #1
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    integral

    If f is continuous on [-1,1] and f(-x) + f(x) = x^2 -2 then the integral from -1 to 1 of f(x)dx = ?
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  2. #2
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    Quote Originally Posted by chaddy View Post
    If f is continuous on [-1,1] and f(-x) + f(x) = x^2 -2 then the integral from -1 to 1 of f(x)dx = ?
    I = \int_{-1}^{1} f(x) \, dx = \int_{-1}^{0} f(x) \, dx + \int_{0}^{1} f(x) \, dx.

    Let x \rightarrow -x in \int_{-1}^{0} f(x) \, dx and you get \int_{-1}^{0} f(x) \, dx = \int_{1}^{0} f(-x) \, (-dx) = \int_{0}^{1} f(-x) \, dx .

    Therefore I = \int_{0}^{1} f(-x) \, dx + \int_{0}^{1} f(x) \, dx = \int_{0}^{1} f(-x) + f(x) \, dx = ......
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