We want to find the exact length of the arc along the curve y=1+6x^(3/2) from (0,0) to (4,49)

Alberanteb4T

Alberanteb4T

Answered question

2022-11-27

We want to find the exact length of the arc along the curve y = 1 + 6 x 3 / 2 from (0,0) to (4,49)
a) Set up the integral that will calculate the arc length.
b)L=?
b) Evaluate the integral exactly.
L=?
c) Use your calculator and approximate the arc length correct to three decimals.
L ?

Answer & Explanation

Aileen Powers

Aileen Powers

Beginner2022-11-28Added 12 answers

The given curve is:
y = 1 + 6 x 3 / 2 a ) L = a b 1 + ( y ) 2 d x
Here a=0, b=4
y = 0 + 6 ( 3 / 2 ) x 3 / 2 1 = 9 x
So, L = 0 4 1 + ( 9 x ) 2 d x = 0 4 1 + 81 x d x = 0 4 ( 1 + 81 x ) 1 / 2 d x = [ ( 1 + 81 x ) 3 / 2 3 / 2 × 81 ] 0 4 = [ 2 243 ( 1 + 81 x ) 3 / 2 ] 0 4 L = [ 2 243 { ( 325 3 / 2 1 ) } ] c ) L 48.206

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