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

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Answer 1 · 2015-06-22T18:08:12

Arc length would be #int_4^9 (sqrt(1+(dy/dx)^2))dx#

= #int_4^9( sqrt(1+36x))dx#

=#[2/3 *1/36 (1+36x)^(3/2)]_4^9#

=#1/54[(343)^(3/2)- (145)^(3/2)]#

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

Answer 2 · 2015-06-23T16:49:27

76.1664

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

Arc length= #1/54[ (1+36x)^(3/2)]_4^9#

= #1/54[ 325 ^(3/2)- 145^(3/2)]#

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