What is the integral from 0 to 2 of pi(8-x^3)^2 ?

The integral from 0 to 2 of pi(8-x^3)^2 is pi 576/7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of pi(8-x^3)^2

\int_{0}^{2} π (8 - x^{3})^{2} d x

π \frac{576}{7}

Decimal Notation

258.50819 \dots

Solution steps

\int_{0}^{2} π (8 - x^{3})^{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}^{2} (8 - x^{3})^{2} d x

Expand

(8 - x^{3})^{2} : 64 - 16 x^{3} + x^{6}

= π \cdot \int_{0}^{2} 64 - 16 x^{3} + x^{6} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{0}^{2} 64 d x - \int_{0}^{2} 16 x^{3} d x + \int_{0}^{2} x^{6} d x)

\int_{0}^{2} 64 d x = 128

\int_{0}^{2} 16 x^{3} d x = 64

\int_{0}^{2} x^{6} d x = \frac{128}{7}

= π (128 - 64 + \frac{128}{7})

Simplify

π (128 - 64 + \frac{128}{7}) : π \frac{576}{7}

= π \frac{576}{7}

x \to - 2 lim (x^{4})

n = 1 \sum \infty (2 n + 1)^{- 6}

9 cos (\frac{2}{5} x)

\int \frac{3 x}{( x ^{2} - 3 ) ^{3}} d x

\frac{d}{d x} (\frac{2 x - 5}{2 x + 5})

What is the integral from 0 to 2 of pi(8-x^3)^2 ?
The integral from 0 to 2 of pi(8-x^3)^2 is pi 576/7