What is the integral from 0 to pi/4 of sin(t)cos(t) ?

The integral from 0 to pi/4 of sin(t)cos(t) is 1/4

Popular >

integral from 0 to pi/4 of sin(t)cos(t)

\int_{0}^{\frac{π}{4}} sin (t) cos (t) d t

\frac{1}{4}

Decimal

0.25

Solution steps

\int_{0}^{\frac{π}{4}} sin (t) cos (t) d t

Apply u-substitution

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

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

Apply the Power Rule

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

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

\frac{2}{2} = \frac{1}{2}

= [\frac{u ^{2}}{2}]_{0}^{\frac{1}{2}}

Compute the boundaries:

\frac{1}{4}

= \frac{1}{4}

\int_{0}^{\infty} e^{- x^{2}} x d x

\int_{0}^{2} 3 e^{x} d x

\int_{1}^{8} \frac{16 x}{x ^{2} + 6} d x

\int_{1}^{e} \frac{[ ln ( x ) ] ^{2}}{x} d x

\int_{3}^{4.3} (12 x^{2} - 6 x + \frac{4}{x}) d x

What is the integral from 0 to pi/4 of sin(t)cos(t) ?
The integral from 0 to pi/4 of sin(t)cos(t) is 1/4