What is f(x) = int x^4-x^2+5 dx if f(3)=-1 ?
1 Answer
Jun 20, 2016
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