Integration with a fraction

omf24

Can someone please help me with this problem. Please see the attached image.

The integration when removing the min and max is also provided, how is the answer x²/2 - x³/6? Do we not do anything with the 1 - 1/2 part? and the +2 part? Are we only looking at (x²-2x)/2?

I appreciate the help.

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mathman

The integrand is x - x²/2.

HallsofIvy

[tex]-\frac{1}{2}\left(x^2- 2x+ 2\right)= -\frac{1}{2}x^2+ x- 1[/tex]
Adding 1 to that gives the integrand
[tex]-\frac{1}{2}x^2+ x[/tex]
as mathman says.

omf24

Thanks, that is exactly what I needed to know.