Hello, Larrioto!

First of all, it isI'm having problems recognizing what is a perfect square and what is not.

For example: .

Can i get a full demonstration of why this is a perfect square and tip to recognize it?nota perfect square . . . Let's start at the very beginning.

We have a function: . . . . . not a perfect square

. . and we want its arc length over some interval (a,b).

We use the formula: .

So we form the expession under the radical . . .

We have: . . . . . not a perfect square

Then: .

.

Hence: .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

So they gave us a rather ugly function,

. . but it produces a simple integral.

I've learned toexpectthis in an Arc Length problem.

But, as far as I know, there's no way torecognizeit in advance.