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 f(-3)=1

:. -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)