# How do you find the arc length of the curve #y=sqrt(x-3)# over the interval [3,10]?

##### 1 Answer

Mar 13, 2018

Arc length will be approximately

#### Explanation:

Recall that arc length of a curve is given by

#A = int_a^b sqrt(1 + (dy/dx)^2) dx#

The derivative of our curve is given by the chain rule as being

#A = int_3^10 sqrt(1 + (1/(2sqrt(x- 3)))^2) dx#

#A = int_3^10 sqrt(1 + 1/(4(x - 3)))dx#

#A = int_3^10 sqrt((4x - 12 + 1)/(4(x -3)))dx#

#A = int_3^10 sqrt((4x - 11)/(4x - 12))dx#

This is a pretty complex integral, so I would solve using a graphing calculator.

Evaluating you should get

Hopefully this helps!