Recent content by 1d20

That's disappointing. Thanks anyway.

I recently saw How the Universe Works, and was impressed by the video of astronaut Don Pettit’s sugar-and-salt experiment. (6 minutes into the show. Put sugar and salt in a plastic bag, and watch as the grains visibly gravitate toward each other in zero-G.) I’m trying to express this process...

Thanks for the help! A final question: I thought all integrating factors must have the p(x) part integrated, but this seems to be an exception. How come?

I've been unable to fully solve this: \frac{dy}{dx} + y = xy^4 The U: u = y^{-3}, so y = u^\frac{-1}{3}, and \frac{dy}{dx} = \frac{-1}{3}u^\frac{-4}{3}\frac{du}{dx} The substitution: \frac{-1}{3}u^\frac{-4}{3}\frac{du}{dx} + u^\frac{-1}{3} = xu^\frac{-4}{3} Simplified: \frac{du}{dx} -...

Thanks; this forum's code is very frustrating. Of course I've thought about it; that's why I'm here. If I hadn't thought about it, I'd have integrated according to my first instinct. Which in this case happened to be mostly right, but obviously I didn't know that. I've had no practice with...

Okay, next question. “For the solid bounded by z = 4 - y^2, y = x, x = 0, z = 0 find the volume using a double integral.” I did this using a triple, but I’m stuck trying to use a double. Converting to cylindrical coordinates, z goes from 0 to 4 - r^2sin^2θ while θ goes from ∏/4 to ∏/2...

I’ve got two questions about two problems. First I just want to confirm that I’m setting up this density integral properly: “Find the mass of the conical solid bounded by z = \sqrt{x^2 + y^2} and x^2 + y^2 + z^2 = 4 if the density at any point is proportional to the distance to the origin. I’m...

Thanks! It was r being in the denominator inside a radical that threw me off. While I'm here, does this forum have a list of all the symbol codes? I'd post here more often if I didn't have to 'cheat' from other threads every time I want to post.

I’m doing a lot of double integrals to find surface area problems, and I don’t think I’m setting them up quite right. For example, “Find the surface area of the portion of the sphere x^2 + y^2 + z^2 = 25 inside the cylinder x^2 + y^2 = 9.” I converted the sphere to a function of z: \sqrt{25...

Preface: This question is a result of personal interest, and has nothing to do with any assignment. Okay here's the deal; I've tutored trig in the past, and I've noticed one thing that a lot of folks have trouble with is the fact that there are two pi radians per circle. (It doesn't help that...

I did the algebra: (x^2 - 6)^2 = x^4 - 12x^2 + 36 (4x-x^2 - 6)^2 = x^4 - 8x^3 + 28x^2 - 48x + 36 (x^4 - 12x^2 + 36) - (x^4 - 8x^3 + 28x^2 - 48x + 36) = 8x^3 - 40x^2 - 48x Then I integrated: \pi\int (8x^3 - 40x^2 - 48x) dx = \pi(2x^4 - (40/3)x^3 - 24x^2) Then I plugged the interval...

Hi all, first time here. Huzzah! Looking for help setting up the integral for this: 1. Find the volume of the solid generated by revolving the region bounded by y = x^2 and y = 4x - x^2 around the line y = 6. 2. V = π ʃ [f(x)]^2 dx 3. I've tried every variation of: π ʃ [(x^2 - 6)^2 - (4x -...