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

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

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

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

2

Solution steps

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

Apply u-substitution

= - 3 \cdot \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

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