2 Finding length of curve problems

1. Jan 24, 2007

Sympathy

1. Find the exact length of the curve analytically by antidifferentiation. You will need to simplify the integrand algebraically before finding an antiderivative.

y = the integral from -2 to x of the SQUARE ROOT (3t^4-1)dt, -2 < x < -1

note that the "<" is actually less than or equal to, don't know how to post that.

For this one, do I just plug the x in? x_x I'm really clueless on how to start

2. Find the length of the curve.

y = the integral of 0 to x of SQUARE ROOT (cos(2t))dt from x = 0 to x = pi/4

The problem with me is I know how to do it in terms of y and x, but I am terrible at parametrics.

Last edited: Jan 24, 2007
2. Jan 25, 2007

Gib Z

Heres the arc length formula:

$$\int_a^b \sqrt{1+\frac{dy}{dx}} dx$$. Sub in the requirements, easy enough to get.

Last edited: Jan 25, 2007
3. Jan 25, 2007

Gib Z

O sorry didnt actually read it through well. For the first one,

$$\int^{-2}_{x} \sqrt{3t^4 -1} dt$$. If there wasn't an X there, but instead a normal number like you normally see, you would find the integral and then sub in b into it, and - the integral with a subbed in. In this case just sub in X.

4. Jan 25, 2007

Gib Z

For the second one, there should be a second parametric equation >.<

5. Jan 25, 2007

Sympathy

how do you actually type in the integral sign and stuff?

6. Jan 25, 2007

drpizza

Here's one source:
http://www.artofproblemsolving.com/LaTeX/AoPS_L_GuideCommands.php [Broken]
which will help with formatting the integrals

And another source for starters: (crash course in LaTeX at these forums:
https://www.physicsforums.com/misc/howtolatex.pdf

Last edited by a moderator: May 2, 2017
7. Jan 25, 2007

drpizza

Oh, and to see specifically how Gib Z did it, click to quote him, and take a look at what he has.

However, the formula has a small mistake in it...
(So, I copied and pasted from the quote so I could change it more simply)
$$\int_a^b \sqrt{1+(\frac{dy}{dx})^2} dx$$.
There's supposed to be a squared in there...

8. Jan 25, 2007

Gib Z

Yes, of course, drpizza's correct...I forget the squared, my bad :p

9. Jan 25, 2007

Gib Z

Btw, rather than actually having to quote me, just click on my latex pictures, that'll show up what I typed to show that code.