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

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

integral from 0 to pi of-3cos^2(x)sin(x)

\int_{0}^{π} - 3 cos^{2} (x) sin (x) d x

- 2

Solution steps

\int_{0}^{π} - 3 cos^{2} (x) sin (x) d x

Take the constant out:

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

= - 3 \cdot \int_{0}^{π} cos^{2} (x) sin (x) d x

Apply u-substitution

= - 3 \cdot \int_{1}^{- 1} - u^{2} d u

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

= - 3 (- \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

= - 3 (- (- \int_{- 1}^{1} u^{2} d u))

Apply the Power Rule

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

Simplify

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

Compute the boundaries:

\frac{2}{3}

= - 3 \cdot \frac{2}{3}

Simplify

= - 2

\int_{0}^{1} 8 cos (\frac{π t}{2}) d t

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

\int_{0}^{1} x^{4} (1 + 2 x^{5})^{3} d x

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

\int_{- 2}^{- 1} \frac{1}{x x ^{2} - 1} d x

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