What is f(x) = int x-e^(x-3)dxf(x)=∫x−ex−3dx if f(0)=-2 f(0)=−2?

1 Answer
Sonnhard
Jul 12, 2018

f(x)=x^2/2-e^(x-3)-2-e^(-3)f(x)=x22−ex−3−2−e−3

Explanation:

using that

int x-e^(x-3) dx=x^2/2-e^(x-3)+C∫x−ex−3dx=x22−ex−3+C
we get that
f(0)=e^(-3)+C=-2f(0)=e−3+C=−2 so

C=-2-e^(-3)C=−2−e−3

we have used that

int xdx=x^2/2+C_1∫xdx=x22+C1

int e^(x-3)dx=e^(x-2)+C_2∫ex−3dx=ex−2+C2

Related questions
See all questions in Evaluating the Constant of Integration
Impact of this question
1444 views around the world
You can reuse this answer
Creative Commons License