What is f(x) = int 5e^(2x)-2e^x-x dx if f(4 ) = 1 ?
1 Answer
Nov 14, 2016
f(x) = 5/2e^(2x) - 2e^x - x^2/2 + 9 - 5/2e^8 + 2e^4
Explanation:
We have
Integrating gives us:
f(x) = 5/2e^(2x) - 2e^x - x^2/2 + C
We know
5/2e^8 - 2e^4 - 16/2 + C = 1
:. C = 9 - 5/2e^8 + 2e^4
Hence,
f(x) = 5/2e^(2x) - 2e^x - x^2/2 + 9 - 5/2e^8 + 2e^4