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

The integral from-2 to 2 of (4-y^2)-(y^2-4) is 64/3

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 (4-y^2)-(y^2-4)

\int_{- 2}^{2} (4 - y^{2}) - (y^{2} - 4) d y

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

\int_{- 2}^{2} 4 - y^{2} - (y^{2} - 4) d y

Simplify

= \int_{- 2}^{2} - 2 y^{2} + 8 d y

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} 2 y^{2} d y + \int_{- 2}^{2} 8 d y

\int_{- 2}^{2} 2 y^{2} d y = \frac{32}{3}

\int_{- 2}^{2} 8 d y = 32

= - \frac{32}{3} + 32

Simplify

- \frac{32}{3} + 32 : \frac{64}{3}

= \frac{64}{3}

\int_{0}^{\infty} y e^{- y x} d x

\int_{0}^{16} 10 x d x

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

\int_{x}^{x^{2}} ln (t) d t

\int_{14}^{14} (x) d x

What is the integral from-2 to 2 of (4-y^2)-(y^2-4) ?
The integral from-2 to 2 of (4-y^2)-(y^2-4) is 64/3