How do you find the arc length of the curve y = 4x^(3/2) - 1y=4x32−1 from [4,9]?

2 Answers
bp
Jun 22, 2015

Arc length would be int_4^9 (sqrt(1+(dy/dx)^2))dx∫94⎛⎝√1+(dydx)2⎞⎠dx

= int_4^9( sqrt(1+36x))dx∫94(√1+36x)dx

=[2/3 *1/36 (1+36x)^(3/2)]_4^9[23⋅136(1+36x)32]94

=1/54[(343)^(3/2)- (145)^(3/2)]154[(343)32−(145)32]

= 1/54[7^(9/2) -(145)^(3/2)]154[792−(145)32]
This can be simplified, if required, to get an approximation, using calculator.

bp
Jun 23, 2015

76.1664

Explanation:

An error has crept into the solution. The correction is as follows:

Arc length= 1/54[ (1+36x)^(3/2)]_4^9154[(1+36x)32]94

= 1/54[ 325 ^(3/2)- 145^(3/2)]154[32532−14532]

This can be simplified, if required as 1/54[ 5859.020- 1746.031]154[5859.020−1746.031]
= 76.1664

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