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5 votes
Find the length L of the curve


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

User Abie
by
8.1k points

1 Answer

7 votes

Answer:

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.

User Yinglin
by
7.7k points

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