What is the integral from 0 to pi of 6xsin(x) ?

The integral from 0 to pi of 6xsin(x) is 6pi

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integral from 0 to pi of 6xsin(x)

\int_{0}^{π} 6 x sin (x) d x

6 π

Decimal Notation

18.84955 \dots

Solution steps

\int_{0}^{π} 6 x sin (x) d x

Take the constant out:

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

= 6 \cdot \int_{0}^{π} x sin (x) d x

Apply Integration By Parts

: [- x cos (x) - \int - cos (x) d x]_{0}^{π}

= 6 [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

= 6 [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= 6 [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= 6 π

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What is the integral from 0 to pi of 6xsin(x) ?
The integral from 0 to pi of 6xsin(x) is 6pi