What is the integral from 0 to pi/2 of cos(φ)sin(φ) ?

The integral from 0 to pi/2 of cos(φ)sin(φ) is 1/2

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integral from 0 to pi/2 of cos(φ)sin(φ)

\int_{0}^{\frac{π}{2}} cos (φ) sin (φ) d φ

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{\frac{π}{2}} cos (φ) sin (φ) d φ

Apply u-substitution

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

= \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}

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What is the integral from 0 to pi/2 of cos(φ)sin(φ) ?
The integral from 0 to pi/2 of cos(φ)sin(φ) is 1/2