Okay I'm understanding this for the most part but am having trouble with what I believe is an algebra step.(adsbygoogle = window.adsbygoogle || []).push({});

Find the length of an arc curve y=x^(3/2) from (1,1) to (2,2sqrt2)

For second part I need to do it in terms of x.

Okay..

Rewritten,

x = g(y) = y^(2/3)

___________________

So,

L= int{ctod} sqrt(1 + [g'(y)]^2) dy

= int{1 to 2sqrt2} sqrt(1 + [2/3*y^(-1/3)]^2) dy

= int{1 to 2sqrt2} sqrt(1 + [4/9*y^(-2/3)] dy

___________________

Because,

g'(y)= 2/3*y^(-1/3)

[g'(y)]^2 = 4/9*y^(-2/3)

___________________

Now,

For inside the square root

1 + [g'(y)^2] = 1 + 4/9*y^(-2/3) = 1 + 4/9y^(2/3)

= 9y^(2/3) + 4 / 9y^(2/3)

___________________

Back to the Formula,

L = int{1 to 2sqrt2) sqrt(9y^(2/3)+ 4 / 9y^(2/3))

= int {1 to 2sqrt2}(1/3)(1/y^(1/3))sqrt(9y^(2/3) + 4) dy

___________________

Where and how do you get (1/3)(1/y^(1/3)) from the statement before?

I know I have to use substitution but I'm confused on that step...

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