# What is the area under the curve y = 2x^{-3} from 6 to 10?

Aug 28, 2015

Area under $y = 2 {x}^{- 3}$ from 6 to 10 is $\frac{4}{225}$

#### Explanation:

The area under the curve $y = 2 {x}^{- 3}$ from 6 to 10 is

${\int}_{6}^{10} 2 {x}^{-} 3 \mathrm{dx}$

$= - 1 \cdot {x}^{-} 2 {|}_{6}^{10}$

$= - 1 \cdot \frac{1}{x} ^ 2 {|}_{6}^{10}$

$= \left(- \frac{1}{10} ^ 2\right) - \left(- \frac{1}{6} ^ 2\right)$

$= \frac{1}{36} - \frac{1}{100}$

$= \frac{4}{225}$ (after a bit of arithmetic)