Hello(adsbygoogle = window.adsbygoogle || []).push({});

Im working on some line integral problems at the moment. The first one is really only a check - I think ive worked it out...

Compute the line integral of the vector field B(r) = x^2 e(sub 1) + y^2 e(sub 2) along a straight line from the origin to the point e(sub 1) + 2 e(sub 2) + 4 e(sub 3). Explain why your answer should be independant of the path of integration.

So quickly - z = 2y = 4x

y = 2x soy^2 = 4x^2->dy = 8x dx

thus B(r) = x^2 e + 4x^2

so we integrate this over 0->1 (as we converted all the bits to x) and thus I end with an answer of 11.

The second part I think reads something like "because the line integral depends only on the arc length", but really thats something I read off wikipedia or somewhere so am not particularly sure about :)

The other question is proving more tricky...

Compute the line integral of a vector field F = xe(sub1) + ye(sub 2) + 2ze(sub 3) along a circular helix between the two points (a,0,0) and (a,0,b) parametrized by r = (a cos phi, a sin phi, (b/2*pi) phi). Can you check your result using a differant path and why? Do so for example using a direct line.

So as before I might go ahead and say x = y = 1/2 z, but then I wouldnt know where to go with the parametric component to the question. Any pointers in this would be great - I think I have to differentiate the parametric part, but then dont know where to go from there (suspect some cross-producting in there, such as int(r x r') but im really not very confident any hypothesis I have!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Line Integrals - Cartesian and Parametric

**Physics Forums | Science Articles, Homework Help, Discussion**