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

1 Answer
Feb 21, 2017

f(x)=-1/4x^4+3/2x^2-4x+3

Explanation:

Integrate each term using the color(blue)"power rule for integration"

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(int(ax^n)=a/(n+1)x^(n+1) ; n≠-1)color(white)(2/2)|)))

rArrint(-x^3+3x-4)dx

f(x)=-1/4x^4+3/2x^2-4x+c

"solve for c, given "f(2)=-3

-3=-4+6-8+crArrc=3

rArrf(x)=-1/4x^4+3/2x^2-4x+3