What is f(x) = int e^(2x)-2e^x+3x dx if f(4 ) = 2 ?

1 Answer
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