en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (y-2)^2

Solution

\int (y - 2)^{2} d y

Solution

\frac{y ^{3}}{3} - 2 y^{2} + 4 y + C

Solution steps

\int (y - 2)^{2} d y

Expand

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

= \int 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 y^{2} d y - \int 4 y d y + \int 4 d y

\int y^{2} d y = \frac{y ^{3}}{3}

\int 4 y d y = 2 y^{2}

\int 4 d y = 4 y

= \frac{y ^{3}}{3} - 2 y^{2} + 4 y

Add a constant to the solution

= \frac{y ^{3}}{3} - 2 y^{2} + 4 y + C

Popular Examples

derivative of ((x^2-5^3)/(x^2+4))

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{x ^{2} + 4})

integral of+4e^{-7x}

\int + 4 e^{- 7 x} d x

(\partial)/(\partial x)(3ze^{xy})

\frac{\partial}{\partial x} (3 z e^{x y})

slope of (4.5)(2.3)slope

(4.5) (2.3)

d/(d{y)}({x}{y}{z})

\frac{d}{d y} (x y z)

Frequently Asked Questions (FAQ)

What is the integral of (y-2)^2 ?
The integral of (y-2)^2 is (y^3)/3-2y^2+4y+C