Consider the function f(x)=9x3−4x5.

Question

Let F(x) be the antiderivative of f(x) with F(1)=0.
Then F(4) =

Answer 1

f(x)=9x³-4x^5
F(x)=∫f(x)dx=(9/4)x^4-(4/6)x^6+C
Given F(1)=0, solve for C and hence
find F(4)

F(1)=(9/4)1^4-(4/6)1^6+C=0
=>
C=(4/6)-9/4=(8-27)/12=-19/12
=>
F(x)=(9/4)x^4-(4/6)x^6-19/12
Find
F(4)