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

The integral from 0 to pi of sin(x)*cos^2(x) is 2/3

Popular >

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

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

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

\int_{0}^{π} sin (x) cos^{2} (x) d x

Apply u-substitution

: \int_{1}^{- 1} - u^{2} d u

= \int_{1}^{- 1} - u^{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{1} - u^{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \int_{- 1}^{1} u^{2} d u)

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{- 1}^{1}

= - (- [\frac{u ^{3}}{3}]_{- 1}^{1})

Simplify

= [\frac{u ^{3}}{3}]_{- 1}^{1}

Compute the boundaries:

\frac{2}{3}

= \frac{2}{3}

\int_{1}^{2} 2 x + 4 x^{4} d x

\int_{0}^{t} u e^{- 2 u} cos (3 u) d u

\int_{0}^{6} x^{5} d x

\int_{- π}^{π} x^{2} sin^{2} (x) d x

\int_{- 3}^{0} (x) d x

What is the integral from 0 to pi of sin(x)*cos^2(x) ?
The integral from 0 to pi of sin(x)*cos^2(x) is 2/3