What is the integral from 0 to pi of xsin(2x) ?

The integral from 0 to pi of xsin(2x) is -pi/2

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integral from 0 to pi of xsin(2x)

\int_{0}^{π} x sin (2 x) d x

- \frac{π}{2}

Solution steps

\int_{0}^{π} x sin (2 x) d x

Apply Integration By Parts

: [\frac{1}{2} (- x cos (2 x) - 2 \cdot \int - \frac{1}{2} cos (2 x) d x)]_{0}^{π}

= [\frac{1}{2} (- x cos (2 x) - 2 \cdot \int - \frac{1}{2} cos (2 x) d x)]_{0}^{π}

\int - \frac{1}{2} cos (2 x) d x = - \frac{1}{4} sin (2 x)

= [\frac{1}{2} (- x cos (2 x) - 2 (- \frac{1}{4} sin (2 x)))]_{0}^{π}

Simplify

[\frac{1}{2} (- x cos (2 x) - 2 (- \frac{1}{4} sin (2 x)))]_{0}^{π} : [\frac{1}{2} (- x cos (2 x) + \frac{1}{2} sin (2 x))]_{0}^{π}

= [\frac{1}{2} (- x cos (2 x) + \frac{1}{2} sin (2 x))]_{0}^{π}

Compute the boundaries:

- \frac{π}{2}

= - \frac{π}{2}

\frac{\partial}{\partial x} (x e^{15 x y})

\frac{\partial}{\partial x} (- y + x + 2)

n = 3 \sum \infty \frac{( - 1 ) ^{n + 1}}{n !}

\int e^{(x^{2})} d x

\int 3 e^{x^{2}} x d x

What is the integral from 0 to pi of xsin(2x) ?
The integral from 0 to pi of xsin(2x) is -pi/2