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 Notation

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}

= [- 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}

8 w^{4} + 3 w^{2} + 7 w

\int (x^{2} - 4 x + 4)^{\frac{4}{3}} d x

\frac{d y}{d x} = \frac{5 x}{6 y}

\int (2 x^{2} + 5 x) e^{3 x} d x

\frac{e ^{- a s}}{s ^{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