(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Calculus - Stokes' theorem

1. The problem statement, all variables and given/known data

I have F in Cartesian coordinates (F is a vector): F = (y , x , x*z) and a curve C given by the quarter-circle in the z-plane z=1 (so t : (cos(t) , sin(t) , 1) for t between 0 and Pi/4).

I have found the line integral, and it equals 1/2.

For fun I wanted to find the same line-integral using Stokes' theorem, so I find the curl of F to be (0 , -z , 0) and dS I find by finding the normalvector, which is the cross-product between n_r and n_t. This gives a z-component (of course) with magnitude r - but then the surface integral is zero?

Where is my error?

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

Dismiss Notice

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: Calculus - Stokes' theorem

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