What is f(x) = int x^2-2xe^(x)dx if f(0)=-2 ?
1 Answer
Apr 13, 2017
Explanation:
Separate the integral.
f(x) = int x^2dx - int 2xe^xdx
The first integral is
f(x) = 1/3x^3 - int 2xe^xdx
We will use integration by parts for the last integral. We let
int 2xe^xdx = 2x(e^x) - int 2e^x
int2xe^xdx = 2xe^x - 2inte^x
int2xe^x = 2xe^x - 2e^x
int2xe^x = 2e^x(x - 1)
We put the integral back together to find
f(x) = 1/3x^3 - 2e^x(x - 1) + C
We must now find the value of
-2 = 1/3(0)^3 - 2e^0(0 - 1) + C
-2 = 0 + 2 + C
C = -4
This means that
Hopefully this helps!