What is the integral of r^2cos(θ) ?

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

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integral of r^2cos(θ)

\int r^{2} cos (θ) d r

\frac{1}{3} r^{3} cos (θ) + C

Solution steps

\int r^{2} cos (θ) d r

Take the constant out:

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

= cos (θ) \cdot \int r^{2} d r

Apply the Power Rule

= cos (θ) \frac{r ^{3}}{3}

Simplify

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

= \frac{1}{3} r^{3} cos (θ)

Add a constant to the solution

= \frac{1}{3} r^{3} cos (θ) + C

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