Line Integrals

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Homework Statement



don't know the line integral latex code but;

[itex]\int[/itex][itex]\underline{r}[/itex][itex]\times[/itex]d[itex]\underline{r}[/itex]

from (a,0,0) to (a,0,2∏b) on the circular helix [itex]\underline{r}[/itex] = (acos(λ), asin(λ), bλ)

The Attempt at a Solution



Its the multiple use of the position vector r in the question thats confusing me. So far i've tried paramaterising the original integral as (r cross dr/dλ)dλ with dr/dλ being the derivative of the circular helix however I am confused as to whether the r in the integral is the same as the one describing the helix.

Am I on the right track or will i need to use another method?
 

Answers and Replies

  • #2
CAF123
Gold Member
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Homework Statement



don't know the line integral latex code but;

[itex]\int[/itex][itex]\underline{r}[/itex][itex]\times[/itex]d[itex]\underline{r}[/itex]

from (a,0,0) to (a,0,2∏b) on the circular helix [itex]\underline{r}[/itex] = (acos(λ), asin(λ), bλ)

The Attempt at a Solution



Its the multiple use of the position vector r in the question thats confusing me. So far i've tried paramaterising the original integral as (r cross dr/dλ)dλ with dr/dλ being the derivative of the circular helix however I am confused as to whether the r in the integral is the same as the one describing the helix.

Am I on the right track or will i need to use another method?
The r given to you is the parametric representation of the helix. It is easy to check that this is a suitable parametrisation.
 

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