Question

Find the length of the arc of y=(2/3)x^(3/2) from x=0 to x=3.

Answer 1

What's stopping you?

Answer 2

What's the formula and how do I do this problem?

Answer 3

Derive the formula here and now. Might as well.

Answer 4

So do I take the derivative?

Answer 5

I said derive, not differentiate. However we probably will need to differentiate.

Answer 6

Consider if you were to partition x, and then plot a punch of x, y points. Draw lines between the points and then use pythagorean theorem to find the approximate length. Add up these sub lengths and you get your approximate arch length.

The exact length is just doing this, but with infinitely small intervals of x. Instead of a sum, you do an integral.

Answer 7

Given the change of x, Dx and the change of y, Dy.... we know that the approximate length would be L ~ sqrt( Dx^2 + Dy^2 )

Answer 8

Isn't it L=sqrt(1+(dy/dx)^2) dx?

Answer 9

You can simplify: L ~ sqrt( Dx^2( 1 + Dy^2/Dx^2) ) ~ Dx sqrt( 1 + Dy^2/Dx^2 )

Answer 10

Let me do that.

Answer 11

When you let Dx -> 0, then Dx -> dx and Dy^2/Dx^2 -> (dy/dx)^2

Answer 12

and our sum becomes an integral

Answer 13

Why are you telling ME formulas but before you were asking ME formulas.

Answer 14

Because I was skeptical. Thanks for the help.