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leonid [27]
3 years ago
5

Find the length L of the curve

Mathematics
1 answer:
ehidna [41]3 years ago
3 0

Answer:

4.647 to the nearest thousandth.

Step-by-step 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.

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