What is the integral from-r to r of pi(r^2-x^2) ?

The integral from-r to r of pi(r^2-x^2) is pi(2r^3-(2r^3)/3)

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integral from-r to r of pi(r^2-x^2)

\int_{- r}^{r} π (r^{2} - x^{2}) d x

π (2 r^{3} - \frac{2 r ^{3}}{3})

Solution steps

\int_{- r}^{r} π (r^{2} - x^{2}) d x

Take the constant out:

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

= π \cdot \int_{- r}^{r} r^{2} - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{- r}^{r} r^{2} d x - \int_{- r}^{r} x^{2} d x)

\int_{- r}^{r} r^{2} d x = 2 r^{3}

\int_{- r}^{r} x^{2} d x = \frac{2 r ^{3}}{3}

= π (2 r^{3} - \frac{2 r ^{3}}{3})

f (x) = 7 e^{x^{2} - 5 x + 8}, at x = 0

(3 x^{2} - 6 x + 6) e^{- 8 x}

y \frac{d y}{d x} = (y^{2} - y) (2 x + 5)

a^{2} - y^{2}

(x^{2} + 9) y^{^{'}} + x y = 0

What is the integral from-r to r of pi(r^2-x^2) ?
The integral from-r to r of pi(r^2-x^2) is pi(2r^3-(2r^3)/3)