What is the integral from 0 to 1 of 1/2 x^2 ?

The integral from 0 to 1 of 1/2 x^2 is 1/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of 1/2 x^2

\int_{0}^{1} \frac{1}{2} x^{2} d x

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

\int_{0}^{1} \frac{1}{2} x^{2} d x

Take the constant out:

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

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

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{1}

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

Compute the boundaries:

\frac{1}{3}

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

Simplify

= \frac{1}{6}

x - 5 - 100

\frac{1}{2 x - 3}

\int θ 4 1 - θ^{2} d θ

\frac{1}{s ^{2} + 9}

\frac{d}{d x} (4 x - \frac{3}{x})

What is the integral from 0 to 1 of 1/2 x^2 ?
The integral from 0 to 1 of 1/2 x^2 is 1/6