What is F(x) = int e^(x-2) - x dx if F(0) = 1 ?

1 Answer
Apr 28, 2017

F(x) = e^(x-2) - 1/2x^2 + 1 - e^(-2)

Explanation:

We have:

F(x) = int \ e^(x-2) - x \ dx

Integrating wrt x we get:

F(x) = e^(x-2) - 1/2x^2 + C

But we know that F(0)=1, and so:

e^(0-2) - 0 + C = 1
:. e^(-2) + C = 1
:. C = 1 - e^(-2)

Hence,

F(x) = e^(x-2) - 1/2x^2 + 1 - e^(-2)