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 (2-x)^5

Solution

\int_{1}^{3} (2 - x)^{5} d x

Solution

0

Solution steps

\int_{1}^{3} (2 - x)^{5} d x

Expand

(2 - x)^{5} : 32 - 80 x + 80 x^{2} - 40 x^{3} + 10 x^{4} - x^{5}

= \int_{1}^{3} 32 - 80 x + 80 x^{2} - 40 x^{3} + 10 x^{4} - x^{5} 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} 32 d x - \int_{1}^{3} 80 x d x + \int_{1}^{3} 80 x^{2} d x - \int_{1}^{3} 40 x^{3} d x + \int_{1}^{3} 10 x^{4} d x - \int_{1}^{3} x^{5} d x

\int_{1}^{3} 32 d x = 64

\int_{1}^{3} 80 x d x = 320

\int_{1}^{3} 80 x^{2} d x = \frac{2080}{3}

\int_{1}^{3} 40 x^{3} d x = 800

\int_{1}^{3} 10 x^{4} d x = 484

\int_{1}^{3} x^{5} d x = \frac{364}{3}

= 64 - 320 + \frac{2080}{3} - 800 + 484 - \frac{364}{3}

Simplify

64 - 320 + \frac{2080}{3} - 800 + 484 - \frac{364}{3} : 0

= 0

Graph

Popular Examples

integral from 2 to 3 of sqrt(x-2)

integral from 1 to 2 of 2^{4x}

integral from-1 to 5 of 3x^2+4x

integral from 0 to 2 of x^3sqrt(9x^4+1)

integral from 0 to 5 of 1/((x-3)^2)

Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of (2-x)^5 ?
The integral from 1 to 3 of (2-x)^5 is 0