What is the integral from 0 to 1 of x*3x^2 ?

The integral from 0 to 1 of x*3x^2 is 3/4

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 x*3x^2

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

\frac{3}{4}

Decimal

0.75

Solution steps

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

Take the constant out:

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

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

Simplify

x x^{2} : x^{3}

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

Apply the Power Rule

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

= 3 [\frac{x ^{4}}{4}]_{0}^{1}

Compute the boundaries:

\frac{1}{4}

= 3 \cdot \frac{1}{4}

Simplify

= \frac{3}{4}

\int_{- \frac{3 π}{4}}^{\frac{π}{3}} sin (x) d x

\int_{0}^{4} y d y

\int_{0}^{π} x (- cos (x) + 1) d x

\int_{0}^{2 π} \frac{π - x}{2} d x

\int_{1}^{2} (7 x^{6} - 3 x^{2} + 2 x) d x

What is the integral from 0 to 1 of x*3x^2 ?
The integral from 0 to 1 of x*3x^2 is 3/4