What is the integral from 0 to 2 of y-(y^2)/4 ?

The integral from 0 to 2 of y-(y^2)/4 is 4/3

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-(y^2)/4

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

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

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

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

\int_{0}^{2} \frac{y ^{2}}{4} d y = \frac{2}{3}

= 2 - \frac{2}{3}

Simplify

2 - \frac{2}{3} : \frac{4}{3}

= \frac{4}{3}

\int_{1}^{2} \frac{x ^{4} + 1}{x ^{5} + 5 x} d x

\int_{- 2}^{2} 4 - x^{2} + x^{3} d x

\int_{1}^{4} (x - 4)^{2} d x

\int_{- 1}^{x} t^{5} d t

\int_{0}^{3} 1 - e^{- 2 x} d x

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