What is the integral from 0 to r of b*r^3+c*r^2 ?

The integral from 0 to r of b*r^3+c*r^2 is (br^4)/4+(cr^3)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to r of br^3+cr^2

\int_{0}^{r} b \cdot r^{3} + c \cdot r^{2} d r

\frac{b r ^{4}}{4} + \frac{c r ^{3}}{3}

Solution steps

\int_{0}^{r} b r^{3} + c r^{2} d r

Apply the Sum Rule:

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

= \int_{0}^{r} b r^{3} d r + \int_{0}^{r} c r^{2} d r

\int_{0}^{r} b r^{3} d r = \frac{b r ^{4}}{4}

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

= \frac{b r ^{4}}{4} + \frac{c r ^{3}}{3}

What is the integral from 0 to r of b*r^3+c*r^2 ?
The integral from 0 to r of b*r^3+c*r^2 is (br^4)/4+(cr^3)/3