Antiderivative

Question

Consider the function f(x)=(7/x^3)-(3/x^5)

-let F(x) be the antiderivative of f(x) with F(1)=0

-Then F(4)= ???????

Answer 1

f(x) = 7x^-3 - 3x^-5

 

F(x) = 7x^-2/(-2) - 3x^-4/(-4) + c = (-7/2)(1/x²) + (3/4)(1/x⁴) + c

 

F(1) = 0 ⇒

 

-7/2 + 3/4 + c = 0

c = 11/4

 

F(x) = (-7/2)(1/x²) + (3/4)(1/x⁴) + 11/4

 

Plug in x = 4 and simplify tho get F(4).  You can finish from here.