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 2 of (x-1)^2

Solution

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

Solution

3

Solution steps

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

Expand

(x - 1)^{2} : x^{2} - 2 x + 1

= \int_{- 1}^{2} x^{2} - 2 x + 1 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}^{2} x^{2} d x - \int_{- 1}^{2} 2 x d x + \int_{- 1}^{2} 1 d x

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

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

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

= 3 - 3 + 3

Simplify

= 3

Graph

Popular Examples

integral from 0 to pi/2 of sin(x-y)

integral from 0 to 1 of x^9e^{-x}

integral from 0 to pi of e^{-x}sin(x)

integral from 3 to 4 of 1/((x+y)^2)

integral from 0 to 3 of (sqrt(x))/(x+1)

Frequently Asked Questions (FAQ)

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