What is F(x) = int 3x^2-e^(2-x) dx if F(0) = 1 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Ratnaker Mehta 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. Answer link Related questions How do you find the constant of integration for intf'(x)dx if f(2)=1? What is a line integral? What is f(x) = int x^3-x if f(2)=4 ? What is f(x) = int x^2+x-3 if f(2)=3 ? What is f(x) = int xe^x if f(2)=3 ? What is f(x) = int x - 3 if f(2)=3 ? What is f(x) = int x^2 - 3x if f(2)=1 ? What is f(x) = int 1/x if f(2)=1 ? What is f(x) = int 1/(x+3) if f(2)=1 ? What is f(x) = int 1/(x^2+3) if f(2)=1 ? See all questions in Evaluating the Constant of Integration Impact of this question 1371 views around the world You can reuse this answer Creative Commons License