I will let you guys off the hook though, my calculus book specifically states that finding arc lengths with the above formula is manually possible only in very rare circumstances. The problems that you work through in the book are specifically chosen because you **can** integrate them without a computer system.

Our lives revolve around it.

The odd thing is the integral can be written as a simple function. Does that garentee it can be integrated manually?

]]>The formula for arc length is ∫ √( 1 + (f'(x))^2 ) dx (from a to b)

y = x^(2/3) so dy/dx =2/3 x^(-1/3) square this and we have:

4/9 x^(-2/3)

so we've found (f'(x))^2

So the length is:

∫ √( 1 + 4/9 x^(-2/3)) dx from x = 0 to x = 8.

I can't seem to integrate this. My book said in a later lesson they'll show how to integrate expressions such as √(1 + 4x^2) (the arc length of x^2) using trigonometric functions, but in the meantime use an approximation when necessary. But the answer to this problem is an exact answer and not an approximation. So there must be a simple way to integrate without trig functions.

Any idea's?

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