What is the integral from 0 to 2 of 2x+x^2-x^3 ?

The integral from 0 to 2 of 2x+x^2-x^3 is 8/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of 2x+x^2-x^3

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

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

= 4 + \frac{8}{3} - 4

Simplify

= \frac{8}{3}

\int_{0}^{5} ∣ 1 - x ∣ d x

\int_{0}^{2} (t - 1) e^{(t - 1)^{2}} d t

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

\int_{0}^{2} (3 t - 1)^{56} d t

\int_{1}^{e^{- x^{2}}} (ln (t))^{4} d t

What is the integral from 0 to 2 of 2x+x^2-x^3 ?
The integral from 0 to 2 of 2x+x^2-x^3 is 8/3