# What is the arc length of #f(x)=x^2/sqrt(7-x^2)# on #x in [0,1]#?

##### 2 Answers

Jun 1, 2018

The arc length of a function

#s=int_a^bsqrt(1+(f'(x))^2)dx#

Here,

Then, the arc length desired is:

#s=int_0^1sqrt(1+(x^2(14-x^2)^2)/(7-x^2)^3)dx#

This has no closed form. Use a calculator to find:

#sapprox1.10458#

Jun 1, 2018

#### Explanation:

We have

so

Multiplying numerator and denominator by

we get

so

Using the Formula

we get by a numerical method