What is f(x) = int (x-1)^3 dx if f(-1) = 1 ?

1 Answer
Jan 3, 2017

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

Explanation:

Let u = x - 1. Then du = dx.

f(x) = int u^3 du

f(x) = 1/4u^4 + C

f(x) = 1/4(x- 1)^4 + C

Now, solve for C knowing that when x= -1, y = 1.

1 = 1/4(-1 - 1)^4 + C

1 = 1/4(16) + C

1 = 4 + C

C = -3

Hopefully this helps!