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

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

= 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

\frac{d}{d x} (9 + 6 x)

\frac{d}{d x} (4 - 2 x^{2})

x^{2} e^{x} - 2 x e^{x} + 7 e^{x}

x \to - 1 lim (x^{2} + 3 x + 2)

3 y^{^{''}} - 14 y^{^{'}} + 8 y = 0

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