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 Notation

- 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}

= [- 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

\int_{- 1}^{2} 3^{x} d x

\int_{1}^{5} \frac{12 ( ln ( x ) ) ^{3}}{x} d x

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

\int_{0}^{a} 1 d x

\int_{- \infty}^{\infty} \frac{1}{2 x ^{2} - 8 x + 40} d x

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