What is f(x) = int -e^(2x)-x dx if f(-3 ) = 1 ?
1 Answer
May 12, 2017
f(x) = -1/2e^(2x) - 1/2x^2 + 11/2+1/2e^(-6)
Explanation:
We have:
f(x) = int \ -e^(2x)-x \ dx
We can integrate this directly to get:
f(x) = -1/2e^(2x) - 1/2x^2+ C
We are given that
:. -1/2e^(-6) - 1/2 9 + C = 1
:. C = 11/2+1/2e^(-6)
Leading to:
f(x) = -1/2e^(2x) - 1/2x^2 + 11/2+1/2e^(-6)