What is the integral from 0 to cos(θ) of 3r^2sin(θ) ?

The integral from 0 to cos(θ) of 3r^2sin(θ) is cos^3(θ)sin(θ)

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integral from 0 to cos(θ) of 3r^2sin(θ)

\int_{0}^{c o s (θ)} 3 r^{2} sin (θ) d r

cos^{3} (θ) sin (θ)

Solution steps

\int_{0}^{c o s (θ)} 3 r^{2} sin (θ) d r

Take the constant out:

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

= 3 sin (θ) \cdot \int_{0}^{c o s (θ)} r^{2} d r

Apply the Power Rule

: [\frac{r ^{3}}{3}]_{0}^{c o s (θ)}

= 3 sin (θ) [\frac{r ^{3}}{3}]_{0}^{c o s (θ)}

Compute the boundaries:

\frac{cos ^{3} ( θ )}{3}

= 3 sin (θ) \frac{cos ^{3} ( θ )}{3}

Simplify

= cos^{3} (θ) sin (θ)

\int_{- 1}^{2} 3 x^{2} + 5 d x

\int_{0}^{3} 4 - y d y

\int_{4}^{5} 2^{- x} d x

\int_{- 2}^{0} (8 x^{3} - 7 x^{2}) d x

\int_{- 2}^{2} 3 - ∣ x ∣ d x

What is the integral from 0 to cos(θ) of 3r^2sin(θ) ?
The integral from 0 to cos(θ) of 3r^2sin(θ) is cos^3(θ)sin(θ)