What is the integral from 0 to pi/3 of cos(x)sin(x) ?

The integral from 0 to pi/3 of cos(x)sin(x) is 3/8

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integral from 0 to pi/3 of cos(x)sin(x)

\int_{0}^{\frac{π}{3}} cos (x) sin (x) d x

\frac{3}{8}

Decimal

0.375

Solution steps

\int_{0}^{\frac{π}{3}} cos (x) sin (x) d x

Apply u-substitution

: \int_{0}^{\frac{3}{2}} u d u

= \int_{0}^{\frac{3}{2}} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{\frac{3}{2}}

= [\frac{u ^{2}}{2}]_{0}^{\frac{3}{2}}

Compute the boundaries:

\frac{3}{8}

= \frac{3}{8}

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What is the integral from 0 to pi/3 of cos(x)sin(x) ?
The integral from 0 to pi/3 of cos(x)sin(x) is 3/8