Find the length L of the curve y = √(x) from the point P(0,0) to the point Q(4,2)​

Question

Find the length L of the curve


`y = √(x)`
from the point P(0,0) to the point Q(4,2)​

Answer 1

4.647 to the nearest thousandth.

Explanation:

The formula for the length of an arc between x = a and x = b is

a

∫ √( 1 + (f'(x))^2) dx

b

Here f(x) = √x so

we have ∫ (√( 1 + (1/2 x^-1/2))^2 ) between x = 0 and x = 4.

= ∫ ( √( 1 + 1/(4x)) dx between x = 0 and x = 4.

This is not easy to integrate but some software I have gives me the following

length = √17 + 1/8 log(33 + 1/8 √17)

= 4.647.