What is f(x) = int (x-1)^3 dx if f(-1) = 1 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Noah G 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! Answer link Related questions How do you find the constant of integration for intf'(x)dx if f(2)=1? What is a line integral? What is f(x) = int x^3-x if f(2)=4 ? What is f(x) = int x^2+x-3 if f(2)=3 ? What is f(x) = int xe^x if f(2)=3 ? What is f(x) = int x - 3 if f(2)=3 ? What is f(x) = int x^2 - 3x if f(2)=1 ? What is f(x) = int 1/x if f(2)=1 ? What is f(x) = int 1/(x+3) if f(2)=1 ? What is f(x) = int 1/(x^2+3) if f(2)=1 ? See all questions in Evaluating the Constant of Integration Impact of this question 1312 views around the world You can reuse this answer Creative Commons License