# [SOLVED] Path Integral

• May 19th 2008, 03:05 PM
maibs89
[SOLVED] Path Integral
Evaluate the path integral intC f ds where f=x +xy and the path C is the curve resulting from the intersection of the cone z=3(x^2+ y^2)^(0.5) and the sphere x^2 + y^2 + z^2 =10. Assume the curve is oriented anticlockwise.

I got the intersection curve to be x^2 + y^2=1. This is a circle, so I parametrise it as c=(cost, sint). Then c'=(-sint, cost). 0<t<1

What do I sub into f? Is it (x,y)=(cost, sint)? But I thought f was a scalar.

I know the path intergal formula is integrate 0<t<1 f(c) * c' dt.

Help!
• May 19th 2008, 03:14 PM
Jhevon
Quote:

Originally Posted by maibs89
Evaluate the path integral intC f ds where f=x +xy and the path C is the curve resulting from the intersection of the cone z=3(x^2+ y^2)^(0.5) and the sphere x^2 + y^2 + z^2 =10. Assume the curve is oriented anticlockwise.

I got the intersection curve to be x^2 + y^2=1. This is a circle, so I parametrise it as c=(cost, sint). Then c'=(-sint, cost). 0<t<1

What do I sub into f? Is it (x,y)=(cost, sint)? But I thought f was a scalar.

I know the path intergal formula is integrate 0<t<1 f(c) * c' dt.

Help!

Use $\oint_C f(x,y)~ds = \int_a^b f(x(t),y(t)) \sqrt{[x'(t)]^2 + [y'(t)]^2}~dt$

Can you continue?