en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

\int_{0}^{2} (4 - x)^{2} d x

Solution

\frac{56}{3}

+1

Decimal

18.66666 \dots

Solution steps

\int_{0}^{2} (4 - x)^{2} d x

Expand

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

= \int_{0}^{2} 16 - 8 x + 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_{0}^{2} 16 d x - \int_{0}^{2} 8 x d x + \int_{0}^{2} x^{2} d x

\int_{0}^{2} 16 d x = 32

\int_{0}^{2} 8 x d x = 16

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 32 - 16 + \frac{8}{3}

Simplify

32 - 16 + \frac{8}{3} : \frac{56}{3}

= \frac{56}{3}

Graph

Popular Examples

derivative of (-2x-y)/(x+3y^2)

d er i v a t i v e \frac{- 2 x - y}{x + 3 y ^{2}}

(dy)/(dx)=((x-3))/((y-3))

\frac{d y}{d x} = \frac{( x - 3 )}{( y - 3 )}

integral of (x+4)(x-2)

\int (x + 4) (x - 2) d x

implicit (dy)/(dx),e^xy=2

im pl i c i t \frac{d y}{d x}, e^{x} y = 2

integral of (2x+5-1/x)

\int (2 x + 5 - \frac{1}{x}) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (4-x)^2 ?
The integral from 0 to 2 of (4-x)^2 is 56/3