What is the integral of rsin(θ) ?

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

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integral of rsin(θ)

\int r sin (θ) d r

\frac{1}{2} r^{2} sin (θ) + C

Solution steps

\int r 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 d r

Apply the Power Rule

= sin (θ) \frac{r ^{2}}{2}

Simplify

sin (θ) \frac{r ^{2}}{2} : \frac{1}{2} r^{2} sin (θ)

= \frac{1}{2} r^{2} sin (θ)

Add a constant to the solution

= \frac{1}{2} r^{2} sin (θ) + C