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

1 Answer
May 16, 2016

I found: f(x)=e^(3x)/3-e^x-4/3

Explanation:

We can solve the integral and write:
f(x)=inte^(3x)dx-inte^xdx=e^(3x)/3-e^x+c
now we need to find c;
we use the fact that f(0)=-2, i.e., we use x=0 and set it equal to -2:
e^(3*0)/3-e^0+c=-2
1/3-1+c=-2
c=1-2-1/3=-4/3
giving your final function as:
f(x)=e^(3x)/3-e^x-4/3