Recent content by alanthreonus

R is the region in the xy-plane that corresponds to the region S in the uv-plane under the transformation given by x = g(u,v), y = h(u,v), and, yes, that is the Jacobian.

Homework Statement Use Green's Theorem to prove for the case f(x,y) = 1 \int\int_R dxdy = \int\int_S |\partial(x,y)/\partial(u,v)|dudv EDIT: R is the region in the xy-plane that corresponds to the region S in the uv-plane under the transformation given by x = g(u,v), y = h(u,v), and the...

Homework Statement Ampere's Law states \int _C \vec{B} \cdot \vec{dr} = \mu_0 \ I . By taking C to be a circle with radius r, show that the magnitude B = |B| of the magnetic field at a distance r from the center of the wire is B = \frac{\mu_0}{2 \pi} \...

Thanks a bunch guys, I got it now. And now I feel dumb for not seeing all these things I missed.

OK, integration by parts gives (-1/2e^(-rho^2))(rho^2+1) Which is evaluated from 0 to infinity, but unless I'm missing something, the limit at infinity is undefined. And something else occurred to me. If I integrate with respect to phi, I'll get -cos(phi), which evaluated from 0 to 2*pi is...

Homework Statement Show that \int^{infinity}_{-infinity}\int^{infinity}_{-infinity}\int^{infinity}_{-infinity}sqrt(x^2+y^2+z^2)e^-^(^x^2^+^y^2^+^z^2^)dxdydz = 2\pi Homework Equations x^2+y^2+z^2 = \rho^2 The Attempt at a Solution I converted to spherical coordinates to get...

Woops, I meant sqrt(2x-x^2)

Homework Statement Convert to polar coordinates to evaluate \int^{2}_{0}\int^{\sqrt(2x-x^2)}_{0}{\sqrt(x^2+y^2)}dydxThe Attempt at a Solution Really I'm just not sure how to convert the limits of integration. I know \sqrt(2x-x^2) is a half-circle with radius 1, but I'm not really sure where...

Homework Statement You wish to travel to the Pleiades (at a distance of 130 pc) in 10 years, according to the clock that you carry. How fast do you have to travel to accomplish this (express the velocity as a fraction of speed of light, v/c)? Homework Equations \Delta T...