What is the integral from 0 to 2 of (x^3)/3+x ?

The integral from 0 to 2 of (x^3)/3+x is 10/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 2 of (x^3)/3+x

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

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

\int_{0}^{2} \frac{x ^{3}}{3} + x 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_{0}^{2} \frac{x ^{3}}{3} d x + \int_{0}^{2} x d x

\int_{0}^{2} \frac{x ^{3}}{3} d x = \frac{4}{3}

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

= \frac{4}{3} + 2

Simplify

\frac{4}{3} + 2 : \frac{10}{3}

= \frac{10}{3}

What is the integral from 0 to 2 of (x^3)/3+x ?
The integral from 0 to 2 of (x^3)/3+x is 10/3