What is f(x) = int (3-x)e^x dx if f(0)=-2 ?

1 Answer
Feb 15, 2016

f(x)=(3-x)e^x+e^x-6

Explanation:

Given f(x)=int(3-x)e^xdx and that f(0)=-2.

Now, in the given function, we can solve using the formula
int(uv)dx=uintvdx-int(frac{d}{dx}(u)*intvdx)dx
Takin u=3-x and v=e^x you'll end up with
int(3-x)e^xdx=(3-x)inte^xdx-int(d/dx(3-x)*inte^xdx)dx
So the answer if you solve the above is f(x)=(3-x)e^x+e^x+c

Now, they have also said that f(0)=-2 which means we're going to have to find out what that c is.
So f(0)=(3-0)e^0+e^0+cimplies-2=3+1+cimpliesc=-6

So, taking it as such, we get the answer as given above.