en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral from-1 to 3 of x^2(x-2)

Solution

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

Solution

\frac{4}{3}

+1

Decimal

1.33333 \dots

Solution steps

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

Expand

x^{2} (x - 2) : x^{3} - 2 x^{2}

= \int_{- 1}^{3} x^{3} - 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_{- 1}^{3} x^{3} d x - \int_{- 1}^{3} 2 x^{2} d x

\int_{- 1}^{3} x^{3} d x = 20

\int_{- 1}^{3} 2 x^{2} d x = \frac{56}{3}

= 20 - \frac{56}{3}

Simplify

20 - \frac{56}{3} : \frac{4}{3}

= \frac{4}{3}

Graph

Popular Examples

integral from-2 to 2 of 7x+5

integral from 4 to 5 of xe^{-x}

integral from-1 to 4 of |x-2|

integral from 0 to pi/4 of 1/(cos(θ))

integral from 0 to 2 of (2t^3+t)

Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of x^2(x-2) ?
The integral from-1 to 3 of x^2(x-2) is 4/3