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Math Help - Calculus !!!!

  1. #1
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    Calculus !!!!

    If f is a continuous function and if F'(x) = f(x) for all real numbers x, then
    3
    ∫ f(2x) dx =
    1


    (A) 2F(3) - 2F(1)
    (B) 1/2F(3) - 1/2F(1)
    (C) 2F(6) - 2(F2)
    (D) F(6) - F(2)
    (E) 1/2F(6) - 1/2 F(2)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by frozenflames
    If f is a continuous function and if F'(x) = f(x) for all real numbers x, then
    3
    ∫ f(2x) dx =
    1


    (A) 2F(3) - 2F(1)
    (B) 1/2F(3) - 1/2F(1)
    (C) 2F(6) - 2(F2)
    (D) F(6) - F(2)
    (E) 1/2F(6) - 1/2 F(2)
    let u=2x, then:
    \int_1^3 f(2x) dx=\int_2^6 f(u) \frac{dx}{du} du =\frac{1}{2}\int_2^6 f(u) du=\frac{1}{2} (F(6)-F(2))
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