What is f(x) = int e^(2x-1)-e^(3x-2)+e^x dxf(x)=∫e2x−1−e3x−2+exdx if f(2) = 3 f(2)=3?

1 Answer
benjidunn
Mar 30, 2016

f(x)=1/2e^(2x-1)-1/3e^(3x-2)+e^x+3.768f(x)=12e2x−1−13e3x−2+ex+3.768

Explanation:

First integrate to obtain f(x)=1/2e^(2x-1)-1/3e^(3x-2)+e^x+cf(x)=12e2x−1−13e3x−2+ex+c
Then substitute f(2)=3f(2)=3 to obtain 3=1/2e^3-1/3e^4+e^2+c3=12e3−13e4+e2+c
Rearrange for c then evaluate: c=3-1/2e^3+1/3e^4-e^2=3.768c=3−12e3+13e4−e2=3.768 (4s.f.)
Thus the original function is f(x)=1/2e^(2x-1)-1/3e^(3x-2)+e^x+3.768f(x)=12e2x−1−13e3x−2+ex+3.768

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