How do you find the antiderivative of #x^2+5x#, if the point (0,5) exists on the graph of the antiderivative?

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Answer 1 · 2014-10-16T17:00:32

By integrating,

#F(x)=int(x^2+5x)dx=1/3x^3+5/2x^2+C#.

Since #f(0)=5#,

#f(0)=1/3(0)^3+5/2(0)^2+C=C=5#.

Hence,

#F(x)=1/3x^3+5/2x^2+5#.

I hope that this was helpful.