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

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

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

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

- \frac{1}{2}

Decimal

- 0.5

Solution steps

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

Apply u-substitution

= \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}

Compute the boundaries:

\frac{1}{2}

= - \frac{1}{2}

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