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

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

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

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

π - 1

Decimal

2.14159 \dots

Solution steps

\int_{\frac{π}{2}}^{π} x sin (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Compute the boundaries:

π - 1

= π - 1

\int_{- 1}^{0} - x^{2} - x d x

\int_{2}^{4} x e^{- \frac{x}{2}} d x

\int_{x}^{2} \frac{6 ( y - x )}{8} d y

\int_{0}^{1} 15 x^{2} d x

\int_{2}^{3} \frac{1}{ln ( x - 1 )} d x

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