What is f(x) = int (x-1)^2+3x dx if f(3)=2 ?

1 Answer
Nov 19, 2016

Simply expand (x- 1)^2 and then integrate using the rule intx^n(dx) = x^(n + 1)/(n + 1) + C.

f(x) = intx^2 - 2x + 1 + 3xdx

f(x) = intx^2 - x + 1dx

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

We can solve for C now.

When x = 3, y = 2:

2 = 2/3(3)^3 - 1/2(3)^2 + 3 + C

2 = 18 - 9/2 + 3 + C

-19 + 9/2= C

-29/2 = C

Hence, f(x) = 2/3x^3 - 1/2x^2 + x - 29/2.

Hopefully this helps!