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

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

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

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

\frac{3}{8}

Solution steps

\int_{0}^{\frac{π}{3}} sin (x) cos (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}

\int_{0}^{2} - x^{2} + 2 x + 3 d x

\int_{1}^{2} \frac{3 ( ln ( x ) ) ^{2}}{x} d x

\int_{0}^{1} 6 x - 6 x^{2} d x

\int_{0}^{2} cos (π x) d x

\int_{1}^{11} \frac{2 ln ( x )}{x} d x

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