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

The integral from 1 to 3 of 1/2 x^2 is 13/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 3 of 1/2 x^2

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

\frac{13}{3}

Decimal Notation

4.33333 \dots

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{26}{3}

= \frac{1}{2} \cdot \frac{26}{3}

Simplify

= \frac{13}{3}

\int_{1}^{4} (\frac{2}{x} - e^{- x}) d x

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

\int_{0}^{1} \frac{1}{64 - x ^{2}} d x

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

\int_{8}^{x} \frac{1}{t} d t

What is the integral from 1 to 3 of 1/2 x^2 ?
The integral from 1 to 3 of 1/2 x^2 is 13/3