What is the integral from 0 to pi of 5xsin(x) ?

The integral from 0 to pi of 5xsin(x) is 5pi

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integral from 0 to pi of 5xsin(x)

\int_{0}^{π} 5 x sin (x) d x

5 π

Decimal

15.70796 \dots

Solution steps

\int_{0}^{π} 5 x sin (x) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{π} x sin (x) d x

Apply Integration By Parts

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

= 5 [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

= 5 [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= 5 [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= 5 π

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\int_{0}^{1} x 2 x^{2} - x^{4} d x

\int_{- 3}^{3} (1 + 9 - x^{2}) d x

\int_{0}^{a} 5 e^{x} d x

\int_{1}^{2} \frac{1}{x ^{2} + 1} d x

What is the integral from 0 to pi of 5xsin(x) ?
The integral from 0 to pi of 5xsin(x) is 5pi