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
F(x) = e^(x-2) - 1/2x^2 + C
But we know that
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)