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

The integral from pi/2 to 2pi of (xsin(x)) is -2pi-1

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

\int_{\frac{π}{2}}^{2 π} (x sin (x)) d x

- 2 π - 1

Decimal

- 7.28318 \dots

Solution steps

\int_{\frac{π}{2}}^{2 π} x sin (x) d x

Apply Integration By Parts

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

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

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

Simplify

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

Compute the boundaries:

- 2 π - 1

= - 2 π - 1

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