What is f(x) = int x^4-x^2+5 dx if f(3)=-1 ?

1 Answer
Jun 20, 2016

1/5x^5-1/3x^3+5x-278/5

Explanation:

To integrate use the color(blue)"power rule"

int(ax^n)dx=(ax^(n+1))/(n+1)

This rule can be applied to each term in the integral.

int(x^4-x^2+5)dx=1/5x^5-1/3x^3+5x+c

where c is the constant of integration

To find c use f(3) = -1

rArr1/5(3)^5-1/3(3)^3+5(3)+c=-1

rArr243/5-9+15+c=-1rArrc=-278/5

rArrF(x)=1/5x^5-1/3x^3+5x-278/5