What is the integral from 0 to 1 of x(4x^3) ?

The integral from 0 to 1 of x(4x^3) is 4/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of x(4x^3)

\int_{0}^{1} x (4 x^{3}) d x

\frac{4}{5}

Decimal

0.8

Solution steps

\int_{0}^{1} x \cdot 4 x^{3} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{1} x x^{3} d x

Simplify

x x^{3} : x^{4}

= 4 \cdot \int_{0}^{1} x^{4} d x

Apply the Power Rule

= 4 [\frac{x ^{5}}{5}]_{0}^{1}

Compute the boundaries:

\frac{1}{5}

= 4 \cdot \frac{1}{5}

Simplify

= \frac{4}{5}

What is the integral from 0 to 1 of x(4x^3) ?
The integral from 0 to 1 of x(4x^3) is 4/5