What is the integral from-3 to-1 of 2/(r^3) ?

The integral from-3 to-1 of 2/(r^3) is -8/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-3 to-1 of 2/(r^3)

\int_{- 3}^{- 1} \frac{2}{r ^{3}} d r

- \frac{8}{9}

Decimal

- 0.88888 \dots

Solution steps

\int_{- 3}^{- 1} \frac{2}{r ^{3}} d r

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{- 3}^{- 1} \frac{1}{r ^{3}} d r

Apply the Power Rule

= 2 [- \frac{1}{2 r ^{2}}]_{- 3}^{- 1}

Compute the boundaries:

- \frac{4}{9}

= 2 (- \frac{4}{9})

Simplify

= - \frac{8}{9}

What is the integral from-3 to-1 of 2/(r^3) ?
The integral from-3 to-1 of 2/(r^3) is -8/9