en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of (y-2)^2

Solution

\int_{0}^{2} (y - 2)^{2} d y

Solution

\frac{8}{3}

+1

Decimal Notation

2.66666 \dots

Solution steps

\int_{0}^{2} (y - 2)^{2} d y

Expand

(y - 2)^{2} : y^{2} - 4 y + 4

= \int_{0}^{2} y^{2} - 4 y + 4 d y

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} y^{2} d y - \int_{0}^{2} 4 y d y + \int_{0}^{2} 4 d y

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

\int_{0}^{2} 4 y d y = 8

\int_{0}^{2} 4 d y = 8

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

Simplify

= \frac{8}{3}

Popular Examples

derivative of (2x+1^2(x^2+x+1))

\frac{d}{d x} ((2 x + 1)^{2} (x^{2} + x + 1))

integral of 1/((x+6)^2)

\int \frac{1}{( x + 6 ) ^{2}} d x

derivative of (2x^2-5x+7^3)

\frac{d}{d x} ((2 x^{2} - 5 x + 7)^{3})

integral of θsin(θ)

\int θ sin (θ) d θ

derivative of (2x^2+2x+2/(sqrt(x)))

\frac{d}{d x} (\frac{2 x ^{2} + 2 x + 2}{x})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (y-2)^2 ?
The integral from 0 to 2 of (y-2)^2 is 8/3