What is the integral from pi to 2pi of (xsin(x)) ?

The integral from pi to 2pi of (xsin(x)) is -3pi

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integral from pi to 2pi of (xsin(x))

\int_{π}^{2 π} (x sin (x)) d x

- 3 π

Decimal

- 9.42477 \dots

Solution steps

\int_{π}^{2 π} x sin (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

= [- x cos (x) + sin (x)]_{π}^{2 π}

Compute the boundaries:

- 3 π

= - 3 π

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What is the integral from pi to 2pi of (xsin(x)) ?
The integral from pi to 2pi of (xsin(x)) is -3pi