Integrating x^2 sin x: Find Exact Value of Abs(-pi/2 to pi/2)

[madhamster]

The question asks me to integrate x^2 sin x dx and then use it to find the exact value of the integration of abs ( x^2 sin x dx) with upper limit of pi/2 and lower limit of -pi/2.

I have found the integration of x^2 sin x dx which is -x^2 cosx + 2xsinX + 2 cosx + C

but after putting in the upper limits and lower limits i get the answer 2pi, where have i gone wrong because my first part is correct but the second part is different from the answer given.

 

[HallsofIvy]

For what values of x is x² sin x positive and for what values of x is it negative? Remember that |a|= a if a is positive and |a|= -a if a is negative. You cannot just evaluate x² cosx + 2xsinX + 2 cosx + C at -pi/2 and pi/2.