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 #