Circular Helix Line Integral: Solving with r and dr/dλ

[ferret123]

Homework Statement

don't know the line integral latex code but;

\int\underline{r}\timesd\underline{r}

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

The Attempt at a Solution

Its the multiple use of the position vector r in the question that's 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?

 

[CAF123]

Homework Statement

don't know the line integral latex code but;

\int\underline{r}\timesd\underline{r}

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

The Attempt at a Solution

Its the multiple use of the position vector r in the question that's 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.