What is the integral from 0 to pi/4 of cos(θ)sin(θ) ?

The integral from 0 to pi/4 of cos(θ)sin(θ) is 1/4

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integral from 0 to pi/4 of cos(θ)sin(θ)

\int_{0}^{\frac{π}{4}} cos (θ) sin (θ) d θ

\frac{1}{4}

Decimal

0.25

Solution steps

\int_{0}^{\frac{π}{4}} cos (θ) sin (θ) d θ

Apply u-substitution

: \int_{0}^{\frac{2}{2}} u d u

= \int_{0}^{\frac{2}{2}} u d u

Apply the Power Rule

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

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

\frac{2}{2} = \frac{1}{2}

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

Compute the boundaries:

\frac{1}{4}

= \frac{1}{4}

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What is the integral from 0 to pi/4 of cos(θ)sin(θ) ?
The integral from 0 to pi/4 of cos(θ)sin(θ) is 1/4