Calculus

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Consider the function
f(x)=(8)/(x^2)−(8)/(x^5)
.
Let F(x) be the antiderivative of f(x) with F(1)=0.

Then F(2) equals ?

  • Calculus -

    F = ∫ 8/x^2 - 8/x^5 dx
    = 8/3 x^3 - 8/6 x^6 + C
    Since F(1) = 0,
    8/3 x^3 - 4/3 x^6 + C = 0
    C = 4/3 - 8/3 = -4/3

    F(x) = 8/3 x^3 - 4/3 x^6 - 4/3
    F(2) = 8/3 (8) - 4/3 (64) = -64

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