What is the integral from 0 to 2 of (x/2)^3 ?

The integral from 0 to 2 of (x/2)^3 is 1/2

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 (x/2)^3

\int_{0}^{2} (\frac{x}{2})^{3} d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{2} (\frac{x}{2})^{3} d x

Simplify

(\frac{x}{2})^{3} : \frac{x ^{3}}{8}

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

Take the constant out:

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

= \frac{1}{8} \cdot \int_{0}^{2} x^{3} d x

Apply the Power Rule

= \frac{1}{8} [\frac{x ^{4}}{4}]_{0}^{2}

Compute the boundaries:

4

= \frac{1}{8} \cdot 4

Simplify

= \frac{1}{2}

\frac{\partial}{\partial x} (a x^{3} + x e^{x} - 1)

\int \frac{x ^{2} + 24}{x ( x - 2 ) ^{3}} d x

\frac{d}{d x} (\frac{e ^{x}}{7 + e ^{x}})

\int \frac{1}{( x + 2 ) ^{2} ( x - 4 )} d x

cos (2 arctan (x))

What is the integral from 0 to 2 of (x/2)^3 ?
The integral from 0 to 2 of (x/2)^3 is 1/2