What is the integral from 0 to r of pi(r^2-x^2) ?

The integral from 0 to r of pi(r^2-x^2) is pi(r^3-(r^3)/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to r of pi(r^2-x^2)

\int_{0}^{r} π (r^{2} - x^{2}) d x

π (r^{3} - \frac{r ^{3}}{3})

Solution steps

\int_{0}^{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_{0}^{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_{0}^{r} r^{2} d x - \int_{0}^{r} x^{2} d x)

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

\int_{0}^{r} x^{2} d x = \frac{r ^{3}}{3}

= π (r^{3} - \frac{r ^{3}}{3})

\int_{0}^{2 π} 1 cos^{2} (x) d x

\int_{- a}^{a} 4 d x

\int_{1}^{3} 4 x - 3 - x^{2} d x

\int_{0}^{1} (ln (2) + y) d y

\int_{2}^{3} x^{3} \cdot arctan (x - 1) d x

What is the integral from 0 to r of pi(r^2-x^2) ?
The integral from 0 to r of pi(r^2-x^2) is pi(r^3-(r^3)/3)