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

The integral from-2 to 2 of (x^2-2)^2 is 112/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{112}{15}

Decimal

7.46666 \dots

Solution steps

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

Expand

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

= \int_{- 2}^{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

= \int_{- 2}^{2} x^{4} d x - \int_{- 2}^{2} 4 x^{2} d x + \int_{- 2}^{2} 4 d x

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

\int_{- 2}^{2} 4 x^{2} d x = \frac{64}{3}

\int_{- 2}^{2} 4 d x = 16

= \frac{64}{5} - \frac{64}{3} + 16

Simplify

\frac{64}{5} - \frac{64}{3} + 16 : \frac{112}{15}

= \frac{112}{15}

What is the integral from-2 to 2 of (x^2-2)^2 ?
The integral from-2 to 2 of (x^2-2)^2 is 112/15