What is the integral from 0 to 2 of pi(x^2+2)^2 ?

The integral from 0 to 2 of pi(x^2+2)^2 is pi 376/15

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(x^2+2)^2

\int_{0}^{2} π (x^{2} + 2)^{2} d x

π \frac{376}{15}

Decimal

78.74925 \dots

Solution steps

\int_{0}^{2} π (x^{2} + 2)^{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} (x^{2} + 2)^{2} d x

Expand

(x^{2} + 2)^{2} : x^{4} + 4 x^{2} + 4

= π \cdot \int_{0}^{2} x^{4} + 4 x^{2} + 4 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} x^{4} d x + \int_{0}^{2} 4 x^{2} d x + \int_{0}^{2} 4 d x)

\int_{0}^{2} x^{4} d x = \frac{32}{5}

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} 4 d x = 8

= π (\frac{32}{5} + \frac{32}{3} + 8)

Join

\frac{32}{5} + \frac{32}{3} + 8 : \frac{376}{15}

= π \frac{376}{15}

\int_{1}^{\frac{3}{2}} (2 - x - \frac{1}{3} x) d x

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

\int_{- 2}^{3} (5 x^{2} - 3 x) d x

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

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

What is the integral from 0 to 2 of pi(x^2+2)^2 ?
The integral from 0 to 2 of pi(x^2+2)^2 is pi 376/15