# How do you find the arc length of the curve y=1+6x^(3/2) over the interval [0, 1]?

##### 1 Answer
Mar 23, 2018

Use the arc length formula.

#### Explanation:

$y = 1 + 6 {x}^{\frac{3}{2}}$

$y ' = 9 \sqrt{x}$

Arc length is given by:

$L = {\int}_{0}^{1} \sqrt{1 + 81 x} \mathrm{dx}$

Integrate directly:

$L = \frac{2}{243} {\left[{\left(1 + 81 x\right)}^{\frac{3}{2}}\right]}_{0}^{1}$

Hence

$L = \frac{2}{243} \left(82 \sqrt{82} - 1\right)$