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

The integral from 0 to 2 of (y^2)/2 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^2)/2

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

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{2} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{0}^{2}

= \frac{1}{2} [\frac{y ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= \frac{1}{2} \cdot \frac{8}{3}

Simplify

= \frac{4}{3}

\int_{1}^{3} \frac{1}{2 x} d x

\int_{9}^{25} \frac{1}{x} d x

\int_{2}^{4} x^{5} d x

\int_{1}^{e^{9}} \frac{1}{x ( 1 + ln ( x ) )} d x

\int_{- 1}^{0} (2 x + x^{2} - x^{3}) d x

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