What is the integral from-2 to 2 of pi(4-x^2)^2 ?

The integral from-2 to 2 of pi(4-x^2)^2 is pi 512/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-2 to 2 of pi(4-x^2)^2

\int_{- 2}^{2} π (4 - x^{2})^{2} d x

π \frac{512}{15}

Decimal Notation

107.23302 \dots

Solution steps

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

Expand

(4 - x^{2})^{2} : 16 - 8 x^{2} + x^{4}

= π \cdot \int_{- 2}^{2} 16 - 8 x^{2} + x^{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_{- 2}^{2} 16 d x - \int_{- 2}^{2} 8 x^{2} d x + \int_{- 2}^{2} x^{4} d x)

\int_{- 2}^{2} 16 d x = 64

\int_{- 2}^{2} 8 x^{2} d x = \frac{128}{3}

\int_{- 2}^{2} x^{4} d x = \frac{64}{5}

= π (64 - \frac{128}{3} + \frac{64}{5})

Join

64 - \frac{128}{3} + \frac{64}{5} : \frac{512}{15}

= π \frac{512}{15}

\frac{\partial}{\partial y} (lo g_{3} (x - y))

\int \frac{( x ^{2} )}{x ^{2} + 6} d x

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = - 2, y^{^{'}} (0) = 4

cos^{2} (8 t)

y = cos (9 x)

What is the integral from-2 to 2 of pi(4-x^2)^2 ?
The integral from-2 to 2 of pi(4-x^2)^2 is pi 512/15