What is f(x) = int x^3-xf(x)=x3x if f(2)=4 f(2)=4?

2 Answers
Jan 12, 2016

f(x)=x^4/4-x^2/2 + 2f(x)=x44x22+2

Explanation:

For solving the problem first integrate the indefinite integral.

f(x)=int quad x^3-x dx

Use rule int quad x^n dx = x^(n+1)/(n+1) + C

f(x)=x^4/4 - x^2/2 + C

We are given f(2)=4
We are going to find C using the given value.

f(2)=(2)^4/4-(2)^2/2+C
4=16/4-4/2+C
4=4-2+C
4=2+C C=2#

Therefore,

f(x)=x^4/4-x^2/2 + 2

f(x)=x^4/4-x^2/2+2

Explanation:

Given: f(x) = int(x^3-x) dx and f(2)=4

f(x)=int(x^3-x)dx = x^4/4-x^2/2+C

f(x)=x^4/4-x^2/2+C

f(2)=4=2^4/4-2^2/2+C

and C=2

therefore f(x)=x^4/4-x^2/2+2