What is the integral from pi/2 to pi of cos(x)sin(x) ?

The integral from pi/2 to pi of cos(x)sin(x) is -1/2

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integral from pi/2 to pi of cos(x)sin(x)

\int_{\frac{π}{2}}^{π} cos (x) sin (x) d x

- \frac{1}{2}

Decimal

- 0.5

Solution steps

\int_{\frac{π}{2}}^{π} cos (x) sin (x) d x

Apply u-substitution

: \int_{1}^{0} u d u

= \int_{1}^{0} u d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{1}

= - [\frac{u ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= - \frac{1}{2}

\int_{0}^{2} \frac{2}{x ^{2} + 4} d x

\int_{1}^{12} 4 e^{0.1 t} d t

\int_{0}^{5} w 25 - w^{2} d w

\int_{0}^{1} e^{- 5 t} d t

\int_{0}^{\infty} x e^{- p x} d x

What is the integral from pi/2 to pi of cos(x)sin(x) ?
The integral from pi/2 to pi of cos(x)sin(x) is -1/2