What is f(x) = int e^(2x)-2e^x+3x dx if f(4 ) = 2 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Steve M Oct 18, 2016 f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + 2e^4 - e^8/2 - 22 Explanation: f(x) = int (e^(2x) - 2e^x + 3x)dx :. f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + c Now f(4)=2 :. e^8/2 - 2e^4 + (3(16))/2 + c = 2 :. e^8/2 - 2e^4 + 24 + c = 2 :. c = 2e^4 - e^8/2 - 22 Hence, f(x) = e^(2x)/2 - 2e^x + (3x^2)/2 + 2e^4 - e^8/2 - 22 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 1557 views around the world You can reuse this answer Creative Commons License