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Math Help - fundamental theorem of calculus definite intergral problems

  1. #1
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    fundamental theorem of calculus definite intergral problems

    1) Find the definite integral from -10 to 10 if the equation is (100-x^2)dx?





    2) f(x) = x if x<1
    1/x if x>or equal to 1
    Find the definite integral from -1 to 7 f(x)dx?
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    Quote Originally Posted by helppalusmath View Post
    1) Find the definite integral from -10 to 10 if the equation is (100-x^2)dx?
    \int_{-10}^{10}(100 - x^2)dx
    It'll be easier to think about if you break it into two integrals.
    \int_{-10}^{10}100dx - \int_{-10}^{10}x^2dx
    The first piece is easy enough to solve, and the second is power rule:
    F(x) = [100x - \frac{x^3}{3}]_{-10}^{10}
    Just solve F(10) - F(-10) and you're set.
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    Newbie EightballLock's Avatar
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    Quote Originally Posted by helppalusmath View Post
    2) f(x) = x if x<1
    1/x if x>or equal to 1
    Find the definite integral from -1 to 7 f(x)dx?
    Piecewise defined functions are integrated in the same manner you would integrate separate functions.
    F(x) = \frac{x^2}{2} + C if x < 1
    F(x) = \ln{x} + C if x \geq 1
    Just treat it as the sum of two integrals, the first piece from (-1, 1) and the second piece from (1, 7)
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