What is F(x) = int 3x^2+e^(2-2x) dx if F(0) = 1 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Alan N. Jan 12, 2017 F(x) = x^3 +e^2/2 (1-e^(-2x)) +1 Explanation: int 3x^2+e^(2-2x) dx = 3intx^2 dx+ e^2 int e^(-2x) dx = 3*x^3/3 + e^2 int e^(-2x) dx int e^(-2x) dx = -1/2e^(-2x) :. F(x) = x^3 - e^2/2 * e^(-2x) +C Since F(0) =1 0^3 - e^2/2 * e^(-2*0) +C =1 -e^2/2 *1 +C =1 C= 1+e^2/2 F(x) = x^3 - e^2/2 * e^(-2x) +1+e^2/2 = x^3 +e^2/2 (1-e^(-2x)) +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 1373 views around the world You can reuse this answer Creative Commons License