What is F(x) = int 3x^2-e^(2-x) dx if F(0) = 1 ?

1 Answer
May 15, 2017

F(x)=x^3+e^(2-x)+1-e^2, or,

F(x)=x^3+e^2(e^-x -1)+1.

Explanation:

F(x)=int3x^2-e^(2-x)dx.

=3intx^2dx-inte^2*e^-xdx,

=3(x^3/3)-e^2inte^-xdx

F(x)=x^3-e^2*(e^-x/-1)+C=x^3+e^(2-x)+C.

But, F(0)=1 rArr 0^3+e^(2-0)+C=1.

rArr C=1-e^2.

Therefore, F(x)=x^3+e^(2-x)+1-e^2, or,

F(x)=x^3+e^2(e^-x -1)+1.