What is the integral from pi to 2pi of 9xsin(x) ?

The integral from pi to 2pi of 9xsin(x) is -27pi

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integral from pi to 2pi of 9xsin(x)

\int_{π}^{2 π} 9 x sin (x) d x

- 27 π

Decimal

- 84.82300 \dots

Solution steps

\int_{π}^{2 π} 9 x sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int_{π}^{2 π} x sin (x) d x

Apply Integration By Parts

= 9 [- x cos (x) - \int - cos (x) d x]_{π}^{2 π}

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

= 9 [- x cos (x) - (- sin (x))]_{π}^{2 π}

Simplify

= 9 [- x cos (x) + sin (x)]_{π}^{2 π}

Compute the boundaries:

- 3 π

= 9 (- 3 π)

Simplify

= - 27 π

What is the integral from pi to 2pi of 9xsin(x) ?
The integral from pi to 2pi of 9xsin(x) is -27pi