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

1 Answer
Jul 25, 2017

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

Use the power rule to integrate.

= -x^4/4+x^2/2-4x+C " " (item 1)

Find C by using the fact that f(2) = -3

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

-4+2-8+C=-3

- 10 +C = -3

C = 7 " " (item 2)

Combining items (1) and (2), we finish with

f(x) = -x^4/4+x^2/2-4x+7