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

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

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

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}

\int_{- 1}^{1} x cos (x) d x

\int_{- π}^{π} x cos (n x) d x

\int_{0}^{π} x^{2} d x

\int_{0}^{π} cos^{2} (θ) sin (θ) d θ

\int_{0}^{π} sin (x) sin (x) d x

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