What is #f(x) = int x^3-2x+e^x dx# if #f(2) = 5 #?

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Answer 1 · 2016-01-16T08:02:58

#f(x)=x^4/4-x^2+e^x-e^2+5#

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

#f(x)=x^4/4-x^2+e^x+C#

#f(2)=5=2^4/4-2^2+e^2+C# first equation

#5=4-4+e^2+C#

#C=5-e^2#

therefore from the first equation

#f(x)=x^4/4-x^2+e^x-e^2+5#