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

The integral from 0 to 3 of (x^2)/2 is 9/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{9}{2}

Decimal Notation

4.5

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

9

= \frac{1}{2} \cdot 9

Simplify

= \frac{9}{2}

\int_{0}^{1} x e^{x^{3}} d x

\int_{- 1}^{8} (- x^{2} + 10 x) d x

\int_{0}^{1} 20 (x^{3} - x^{4}) d x

\int_{0}^{1} (5 x^{4} - 3 x^{2} + 1) d x

\int_{\frac{- π}{2}}^{\frac{π}{2}} sin (2 x) d x

What is the integral from 0 to 3 of (x^2)/2 ?
The integral from 0 to 3 of (x^2)/2 is 9/2