What is f(x) = int e^(2x)-e^x+x dx if f(4 ) = 2 ?

1 Answer
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