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 (1-x)^3

Solution

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

Solution

- \frac{1}{4}

+1

Decimal

- 0.25

Solution steps

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

Expand

(1 - x)^{3} : 1 - 3 x + 3 x^{2} - x^{3}

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

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

\int_{1}^{2} 3 x d x = \frac{9}{2}

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} x^{3} d x = \frac{15}{4}

= 1 - \frac{9}{2} + 7 - \frac{15}{4}

Simplify

1 - \frac{9}{2} + 7 - \frac{15}{4} : - \frac{1}{4}

= - \frac{1}{4}

Graph

Popular Examples

integral from 1 to e of piln^2(y)

integral from 0 to pi/2 of cos(1/2 x)

integral from 0 to 4 of (5x^2-6x+2)

integral from 0 to θ of (2x^3)/(θ^2)

integral from 1 to 3 of (2)

Frequently Asked Questions (FAQ)

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