Recent content by bawbag

It's just occurred to me that I completed the square incorrectly. So please ignore that part :D. Also, I feel like cylindrical coordinates might be helpful here, but when I change the integral, it seems to get even worse. Any assistance would be appreciated!

Homework Statement Find the area of the cylinder x^2 + y^2 -y = 0 inside the sphere x^2 + y^2 +z^2 =1 Homework Equations dA = sec \gamma dydz where sec \gamma = \frac{|\nabla \phi|}{|\partial \phi/ \partial x|} The Attempt at a Solution The method shown in this section is to...

Thanks, I thought as much. I know how to do it using the spherical polars, but I was just curious as to whether the surface integral method worked as well. Every day's a school day. Thanks again!

Given a sphere x^2 + y^2 + z^2 = a^2 how would I derive the surface area by using surface integrals? The method I've tried is as follows: dA = sec\ \gamma \ dxdy where gamma is the angle between the tangent plane at dA and the xy plane. sec \gamma = \frac{|\nabla \varphi|}{\partial \varphi...

How would you solve this problem using direct integration across the diagonal? I can't seem to figure out how to get the distance from the diagonal axis. Thanks

Gotcha, I figured it would be something simple like that! Thanks a lot!

Homework Statement A force of 500N is measured with a possible error of 1N. Its component in a direction 60° away from its line of action is required, where the angle is subject to an error of 0.5°. What (approximately) is the largest possible error in the component? Homework Equations...

I did use the steps you suggested, jaytech. As for why it works, I imagine that I should be able to reach the solution from any starting point, with proper application of the chain rule/product rule, but arranging it as you suggested means I can skip over a lengthy simplification process after...

Figured it out. Thanks guys. Turns out I laid it out the way jaytech said, but didn't use the product rule properly so I abandoned that method and tried it another way, which lead to that whole mess. Whoops! Thanks to everyone who helped!

That was a typo, my bad. So after sorting the minus sign, I'm left with essentially what I had before, but I can't see anyway of reducing 4r^{2} tan \theta sin^{2} \theta + 4r^{2} sin \theta cos \theta to 4r^{2} tan \theta without ending up with a huge mess. Sorry for being dense :P

Thanks! I used the product rule to differentiate, but I still think I'm missing something. My working is as follows: z = x2 + 2r2 sin2 θ [SIZE="4"]\left(\frac{\partial z}{\partial \theta}\right)_{x} = [SIZE="4"]\frac{\partial}{\partial \theta}2r^{2}sin^{2}\theta [SIZE="4"]=...

Homework Statement if z = x2 + 2y2 , x = r cos θ , y = r sin θ , find the partial derivative [SIZE="4"]\left(\frac{\partial z}{\partial \theta}\right)_{x} Homework Equations z = x2 + 2y2 x = r cos θ y = r sin θ The Attempt at a Solution The textbook says that the equation...

This problem is from Boas Mathermatical Methods 3ed. Section 16, problem 1. Show that if the line through the origin and the point z is rotated 90° about the origin, it becomes the line through the origin and the point iz. Use this idea in the following problem: Let z = ae^iωt be the...