What is the integral from 0 to b of pix^2 ?

The integral from 0 to b of pix^2 is (pib^3)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to b of pix^2

\int_{0}^{b} π x^{2} d x

\frac{π b ^{3}}{3}

Solution steps

\int_{0}^{b} π x^{2} d x

Take the constant out:

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

= π \cdot \int_{0}^{b} x^{2} d x

Apply the Power Rule

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

= π [\frac{x ^{3}}{3}]_{0}^{b}

Compute the boundaries:

\frac{b ^{3}}{3}

= π \frac{b ^{3}}{3}

Simplify

= \frac{π b ^{3}}{3}

\int_{0}^{π} 1 + x^{2} d x

\int_{3}^{6} - 5 x + 6 d x

\int_{1}^{7} \frac{1}{5 x} d x

\int_{\frac{π}{6}}^{\frac{π}{3}} sin (θ) d θ

\int_{- 3}^{0} 2 x + 3 d x

What is the integral from 0 to b of pix^2 ?
The integral from 0 to b of pix^2 is (pib^3)/3