Line Integral with changing variables

calccrypto · 2010-10-06 01:07:47

How do you change variables properly to get the line integral of any f(x,y,z) on any curve C modeled by r(t)??? Im so lost!

bobbym · 2010-10-06 06:06:24

Hi calccrypto;

I am the worst in the world with line integrals. How about posting a specific problem and maybe we can get through it together.

calccrypto · 2010-10-06 06:55:02

Hi bobbym! I got this question:

C modeled by r(t) = (t, 3t^2, 6t^3)
and
f(x,y,z) = x y z^2
compute the line integral of f along C as modeled by r(t)

so far, i have only gotten r'(t) = (1, 6t, 18t^2) and f(t) = 18t^6. I dont know how to continue. all i know is the answer is 864/5

Last edited by calccrypto (2010-10-06 07:05:16)

bobbym · 2010-10-06 07:42:23

Hi;

How did you get 18t^6 for f(r(t))?

Did they give you some range for t?

Like maybe 0 <= t <= 1 ?

Take a look here for some general info that might help.

http://calculus.mindsay.com/section_172 … egrals.mws

calccrypto · 2010-10-06 09:15:50

i just replaced the components of r for (x,y,z) and multiplied.

and yep. I forgot to put in the limits, which are 0<= t <= 1 like you guessed

bobbym · 2010-10-06 09:24:06

Hi;

If I guessed the interval then you did not do f(r(t)) right. Want to try it again?

calccrypto · 2010-10-06 09:34:43

i dont know how to continue at all

bobbym · 2010-10-06 10:19:48

Hi;

This is what I did:

Please check the work as I have not done one of these in years and my notes on them are sketchy.

calccrypto · 2010-10-06 12:45:38

oh.. thats what you meant in that previous post. wow. i fail. shoot me

Last edited by calccrypto (2010-10-06 12:46:45)

bobbym · 2010-10-06 14:06:32

Hi cal;

No shooting allowed here. Had my brother check it, he said this is a book problem that he remembers but he can not remember where.

calccrypto · 2010-10-06 23:22:45

No wonder! I forgot to square the z component.

bobbym · 2010-10-06 23:49:30

Hi;

Use this formula when you are given a line integral where everything has already been parametized like r(t).

It is all covered in the link I posted. This link here will provide more and probably what you will be doing soon.

http://ocw.mit.edu/courses/mathematics/ … s/embed30/

calccrypto · 2010-10-11 13:15:04

what happens if f returns a vector?

bobbym · 2010-10-11 14:12:13

Hi calccrypto;

I do not see how that can happen from the above formula.

calccrypto · 2010-10-11 23:15:54

i meant a generic question. instead of xyz^2, say the output of f was something like (xy,yz,xz) or something. then what?

bobbym · 2010-10-12 07:11:36

Hi calccrypto;

You mean when you substitute x,y,z, in f(x,y,z)?

calccrypto · 2010-10-12 15:32:09

no i meant instead of

f(x,y,x) = scalar value like xyz

the equation is

f(x,y,z) = vector, like (xy,yz,xz)

but i think i got it

Math Is Fun Forum

#1 2010-10-06 01:07:47

Line Integral with changing variables

#2 2010-10-06 06:06:24

Re: Line Integral with changing variables

#3 2010-10-06 06:55:02

Re: Line Integral with changing variables

#4 2010-10-06 07:42:23

Re: Line Integral with changing variables

#5 2010-10-06 09:15:50

Re: Line Integral with changing variables

#6 2010-10-06 09:24:06

Re: Line Integral with changing variables

#7 2010-10-06 09:34:43

Re: Line Integral with changing variables

#8 2010-10-06 10:19:48

Re: Line Integral with changing variables

#9 2010-10-06 12:45:38

Re: Line Integral with changing variables

#10 2010-10-06 14:06:32

Re: Line Integral with changing variables

#11 2010-10-06 23:22:45

Re: Line Integral with changing variables

#12 2010-10-06 23:49:30

Re: Line Integral with changing variables

#13 2010-10-11 13:15:04

Re: Line Integral with changing variables

#14 2010-10-11 14:12:13

Re: Line Integral with changing variables

#15 2010-10-11 23:15:54

Re: Line Integral with changing variables

#16 2010-10-12 07:11:36

Re: Line Integral with changing variables

#17 2010-10-12 15:32:09

Re: Line Integral with changing variables

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