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What is #f(x) = int x-e^(x-3)dx# if #f(0)=-2 #?

1 Answer

Jul 12, 2018

#f(x)=x^2/2-e^(x-3)-2-e^(-3)#

Explanation:

using that

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

#C=-2-e^(-3)#

we have used that

#int xdx=x^2/2+C_1#

#int e^(x-3)dx=e^(x-2)+C_2#

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