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

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

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

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_{0}^{π} (1 - sin^{3} (θ)) d θ

\int_{- π}^{π} x sin (x) d x

\int_{0}^{π} sin^{3} (θ) d θ

\int_{0}^{π} (1 - sin^{3} (x)) d x

\int_{0}^{3} x + 3 d x

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