What is f(x) = int e^(2x)-e^x+x dx if f(4 ) = 2 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Ratnaker Mehta Jul 4, 2016 f(x)=e^(2x)/2-e^x+x^2/2+e^4-e^8/2-6 Explanation: Let I=int(e^(2x)-e^x+x)dx=e^(2x)/2-e^x+x^2/2+C, C is a constant of integration. To determine C, we are given the cond. that f(4)=2. Now, f(x)=I=e^(2x)/2-e^x+x^2/2+C. Hence, f(4)=2 rArr e^8/2-e^4+8+C=2 rArr C=e^4-e^8/2-6. Sub.ing this value of C in I, we get, f(x)=e^(2x)/2-e^x+x^2/2+e^4-e^8/2-6 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 1338 views around the world You can reuse this answer Creative Commons License