Consider the function f(x)=9/x^22−9/x^5.

Question

Let F(x) be the antiderivative of f(x) with F(1)=0.
Then F(3) equals= ???

Answer 1

F(x) = ∫ f(x) dx = 9∫(1/x^22 - 1/x^5) dx = 9(-1/21 * 1/x^21 + 1/4 * 1/x^4) + C
since F(1) = 0, 9(-1/21 + 1/4)+C = 0, so C = -51/28
F(x) = 9(-1/21 * 1/x^21 + 1/4 * 1/x^4) - 51/28
Now find F(3)