What is the integral from-3 to 3 of (|y-2|)^3 ?

The integral from-3 to 3 of (|y-2|)^3 is 313/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-3 to 3 of (|y-2|)^3

\int_{- 3}^{3} (∣ y - 2 ∣)^{3} d y

\frac{313}{2}

Decimal

156.5

Solution steps

\int_{- 3}^{3} ∣ y - 2 ∣^{3} d y

Eliminate Absolutes

= \int_{- 3}^{2} (- y + 2)^{3} d y + \int_{2}^{3} (y - 2)^{3} d y

\int_{- 3}^{2} (- y + 2)^{3} d y = \frac{625}{4}

\int_{2}^{3} (y - 2)^{3} d y = \frac{1}{4}

= \frac{625}{4} + \frac{1}{4}

Simplify

\frac{625}{4} + \frac{1}{4} : \frac{313}{2}

= \frac{313}{2}

What is the integral from-3 to 3 of (|y-2|)^3 ?
The integral from-3 to 3 of (|y-2|)^3 is 313/2