How do you find the length of the curve for y=2x^(3/2) fro (0, 4)?

cleisiogwro

cleisiogwro

Answered question

2023-01-26

How to find the length of the curve for y = 2 x 3 2 for (0, 4)?

Answer & Explanation

Remington Lynch

Remington Lynch

Beginner2023-01-27Added 4 answers

Answer: S = 1 6 ( ( 37 ) 3 2 - 1 )
Given equation is f ( x ) = 2 x 3 2 .
We are given the task to find the length of the curve of the given equation in the interval (0,4).
The equation to find length of the curve is S = 0 4 1 + f ( x ) 2 d x
Thus, the derivative of the given equation will be
f ( x ) = 2 d d x ( x 3 2 ) = 2 3 2 x 3 2 - 1 = 3 x 1 2
Therefore, substituting for f'(x), S = 0 4 1 + 9 x d x
Taking 9 x = t d x = d t 9 and that at x = 0 t = 0 and x = 4 t = 36
Thus, the given integral becomes S = 1 9 0 36 1 + t d t
Therefore, S = 3 1 2 1 9 3 ( 1 + t ) 3 2 0 36
I get the above result by applying limits and totaling.

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