So I'm tutoring this girl in Calculus....

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DrPizza

Administrator Elite Member Goat Whisperer
Mar 5, 2001
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www.slatebrookfarm.com
Calc is easy, so are differential equations.
Pics?

That depends on the teacher. One of today's problems was to find the arclength of y=x² from x=0 to x=1. If calculus is "easy", then you'll have no problem doing that problem by hand, right?
 

MotF Bane

No Lifer
Dec 22, 2006
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That depends on the teacher. One of today's problems was to find the arclength of y=x² from x=0 to x=1. If calculus is "easy", then you'll have no problem doing that problem by hand, right?

Let me find my book, look up how to do an arclength problem, and I'll get back to you on that. :p
 

Arcadio

Diamond Member
Jun 5, 2007
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That depends on the teacher. One of today's problems was to find the arclength of y=x² from x=0 to x=1. If calculus is "easy", then you'll have no problem doing that problem by hand, right?

Now you've got me curious...
 

MegaVovaN

Diamond Member
May 20, 2005
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That depends on the teacher. One of today's problems was to find the arclength of y=x² from x=0 to x=1. If calculus is "easy", then you'll have no problem doing that problem by hand, right?

Arclength part is easy. it is
integral of sqrt (1^2+(2x)^2) from 0 to 1

2x came from deriving x^2

Difficult part is integrating that messy square root. Need some nasty trig substitutions there.

Using a calculator, answer is ~1.48

Am I right Dr. Pizza?
 

Farmer

Diamond Member
Dec 23, 2003
3,334
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That depends on the teacher. One of today's problems was to find the arclength of y=x² from x=0 to x=1. If calculus is "easy", then you'll have no problem doing that problem by hand, right?

I don't remember this, but I believe this is correct. It's probably not the easiest way to do it, but you don't have to search for trig substitutions. Pardon me because it's been like 4 years since I've taken any calculus.

gif.latex


gif.latex


gif.latex


gif.latex


Algebra reaches the form in first line. And the limit is 0 to 45 degrees, since arctan(1/1) = 45 degrees. You can know look up this integral in your favorite handbook.
 
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DrPizza

Administrator Elite Member Goat Whisperer
Mar 5, 2001
49,601
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www.slatebrookfarm.com
Arclength part is easy. it is
integral of sqrt (1^2+(2x)^2) from 0 to 1

2x came from deriving x^2

Difficult part is integrating that messy square root. Need some nasty trig substitutions there.

Using a calculator, answer is ~1.48

Am I right Dr. Pizza?

Using the calculator to arrive at that solution isn't doing calculus. Nasty trig substitutions? Nahhh, the trig substitution is pretty simple. Replace x with 1/2 tan theta. If I recall correctly off the top of my head, you wind up with the integral of secant^3.

And, that's another fun one to do by hand.

Big :) to switching to polar coordinates. My students haven't gotten to working with polar coordinates yet; it's just calc I. But a :( to using a handbook. Where's the challenge in that??
 

Farmer

Diamond Member
Dec 23, 2003
3,334
2
81
Using the calculator to arrive at that solution isn't doing calculus. Nasty trig substitutions? Nahhh, the trig substitution is pretty simple. Replace x with 1/2 tan theta. If I recall correctly off the top of my head, you wind up with the integral of secant^3.

And, that's another fun one to do by hand.

Big :) to switching to polar coordinates. My students haven't gotten to working with polar coordinates yet; it's just calc I. But a :( to using a handbook. Where's the challenge in that??

Yeah my expression above is missing a term. I did not account for the variation in the radial direction, in which case instead of

gif.latex


It should be the norm of the polar 2-vector

gif.latex


It's not as easy as I had thought.
 
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MotF Bane

No Lifer
Dec 22, 2006
60,801
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Spilled soda again while tutoring?


--> Beefpile (~mbeefpile@cloaked.wi.rr.com) has joined #themacmind
<anamexis> and it exploded
<anamexis> ALMOST all over my keyboard
<anamexis> but I got it away just in time
<-- Beefpile has quit (sick fuckers)
 

Avalon

Diamond Member
Jul 16, 2001
7,571
178
106
I misread the title as "So I'm torturing this girl in Calculus"...must be the dyslexia.