What is the integral from 0 to pi of 4xsin(x) ?

The integral from 0 to pi of 4xsin(x) is 4pi

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integral from 0 to pi of 4xsin(x)

\int_{0}^{π} 4 x sin (x) d x

4 π

Decimal

12.56637 \dots

Solution steps

\int_{0}^{π} 4 x sin (x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{π} x sin (x) d x

Apply Integration By Parts

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

= 4 [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

= 4 [- x cos (x) - (- sin (x))]_{0}^{π}

Simplify

= 4 [- x cos (x) + sin (x)]_{0}^{π}

Compute the boundaries:

π

= 4 π

\int_{0}^{π} e^{- s x} sin (x) d x

\int_{0}^{π} e^{c o s (x)} d x

\int_{0}^{3} 2 x + 3 d x

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

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

What is the integral from 0 to pi of 4xsin(x) ?
The integral from 0 to pi of 4xsin(x) is 4pi