What is the integral of r^2sin(θ) ?

The integral of r^2sin(θ) is 1/3 r^3sin(θ)+C

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integral of r^2sin(θ)

\int r^{2} sin (θ) d r

\frac{1}{3} r^{3} sin (θ) + C

Solution steps

\int r^{2} sin (θ) d r

Take the constant out:

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

= sin (θ) \cdot \int r^{2} d r

Apply the Power Rule

: \frac{r ^{3}}{3}

= sin (θ) \frac{r ^{3}}{3}

Simplify

sin (θ) \frac{r ^{3}}{3} : \frac{1}{3} r^{3} sin (θ)

= \frac{1}{3} r^{3} sin (θ)

Add a constant to the solution

= \frac{1}{3} r^{3} sin (θ) + C

\int sin^{2} (\frac{1}{2}) x d x

(- 4, 2), (- 9, - 10)

\int \frac{1}{- v ^{2} + 1} d v

8 csc (5 x^{4} - 8 x + 6)

n = 0 \sum \infty - \frac{1}{3 ^{n}}

What is the integral of r^2sin(θ) ?
The integral of r^2sin(θ) is 1/3 r^3sin(θ)+C