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

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

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integral from-r to r of r^2-x^2

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

2 r^{3} - \frac{2 r ^{3}}{3}

Solution steps

\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

= \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}

= 2 r^{3} - \frac{2 r ^{3}}{3}

\int_{1}^{- x} 1 + t^{2} d t

\int_{- 3}^{3} 18 - x^{2} d x

\int_{0}^{1} e^{- s t} (t - 1) d t

\int_{- 2}^{0} \frac{1}{( x + 1 ) ^{\frac{1}{3}}} d x

\int_{0}^{3} 2 x d x

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