en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

\int_{2}^{5} (x - 4)^{2} d x

Solution

3

Solution steps

\int_{2}^{5} (x - 4)^{2} d x

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{2}^{5} x^{2} - 8 x + 16 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_{2}^{5} x^{2} d x - \int_{2}^{5} 8 x d x + \int_{2}^{5} 16 d x

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 8 x d x = 84

\int_{2}^{5} 16 d x = 48

= 39 - 84 + 48

Simplify

= 3

Graph

Popular Examples

derivative of (tan(x-x)/(x^3))

\frac{d}{d x} (\frac{tan ( x ) - x}{x ^{3}})

integral of x^3sqrt(x^2+18)

\int x^{3} x^{2} + 18 d x

derivative of 2cos(cot(2x+1))

\frac{d}{d x} (2 cos (cot (2 x + 1)))

limit as x approaches-7+of sqrt(1/(x+7))

x \to - 7 + lim (\frac{1}{x + 7})

integral from 2 to 4 of 3e^{3x}

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

Frequently Asked Questions (FAQ)

What is the integral from 2 to 5 of (x-4)^2 ?
The integral from 2 to 5 of (x-4)^2 is 3