What is the integral from pi/2 to pi of θsin(θ) ?

The integral from pi/2 to pi of θsin(θ) is pi-1

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integral from pi/2 to pi of θsin(θ)

\int_{\frac{π}{2}}^{π} θ sin (θ) d θ

π - 1

Decimal Notation

2.14159 \dots

Solution steps

\int_{\frac{π}{2}}^{π} θ sin (θ) d θ

Apply Integration By Parts

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

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

\int - cos (θ) d θ = - sin (θ)

= [- θ cos (θ) - (- sin (θ))]_{\frac{π}{2}}^{π}

Simplify

= [- θ cos (θ) + sin (θ)]_{\frac{π}{2}}^{π}

Compute the boundaries:

π - 1

= π - 1

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What is the integral from pi/2 to pi of θsin(θ) ?
The integral from pi/2 to pi of θsin(θ) is pi-1