What is the integral from pi to 5pi of x^2sin(x) ?

The integral from pi to 5pi of x^2sin(x) is 24pi^2

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integral from pi to 5pi of x^2sin(x)

\int_{π}^{5 π} x^{2} sin (x) d x

24 π^{2}

Decimal

236.87050 \dots

Solution steps

\int_{π}^{5 π} x^{2} sin (x) d x

Apply Integration By Parts

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{π}^{5 π}

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= [- x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))]_{π}^{5 π}

Simplify

= [- x^{2} cos (x) + 2 (x sin (x) + cos (x))]_{π}^{5 π}

Compute the boundaries:

24 π^{2}

= 24 π^{2}

What is the integral from pi to 5pi of x^2sin(x) ?
The integral from pi to 5pi of x^2sin(x) is 24pi^2