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

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

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{\frac{π}{2}} sin (x) cos (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}^{2} \frac{1}{( 1 - x ) ^{2}} d x

\int_{1}^{3} (x + 1)^{4} - (x + 1)^{3} d x

\int_{0}^{6} \frac{1}{4 - x} d x

\int_{- 3}^{3} x d x

\int_{0}^{\frac{π}{6}} \frac{sin ( t )}{cos ^{2} ( t )} d t

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