Recent content by LHC

First of all, I'd like to thank you for your quick reply. However, I'm not quite sure if I understand you correctly. Ok, so the battery's emf is 6V, internal resistance is 0.6 Ohms, and the circuit's net resistance is 7.20 Ohms. When you said: I took that as...the total circuit has a...

There's a problem in my textbook where it gives the emf of a battery, its internal resistance, and the net resistance of the circuit that it is connected to. Then it asks for the terminal voltage. Actually, this is just a problem set (not exactly a textbook), so it doesn't teach me from...

Ohhh...*LED above head suddenly flickers*...I get it. I had the wrong length of the shell! Thanks for explaining that to me. =D

I just found out that I get the answer if I do this: V = \int_{\frac{1}{4}}^{1} 2\pi \ y\ (\frac{1}{y} - 1) dy + \pi \times (\frac{1}{4})^2 \times 3 And that's basically taking shells from y = 1/4 to y = 1, then adding that cylinder that's left behind (from x = 1 to x = 1, and...

I've encountered a weird problem in my text...somewhat by accident =P My text only covers volumes of revolution through the disk method, and one of the questions was: Find the volume of the solid obtained when the given region is rotated about the x-axis. c) Under y = 1/x from 1 to 4 Using...

Thanks, konthelion and HallsofIvy, for your help. HallsofIvy, when you said "Be careful here. One of the equations reduces to 2(a-1)y= 0 which gives y= 0 provided a is not equal to 1. If a= 1, that equation is 0= 0 which is true no matter what y is. That's the case where there are an infinite...

Homework Statement List the conditions of "a" under which the system: x + ay - z = 1 -x + (a-2) y + z = -1 2x + 2y (a-2) z = 1 i) Has no solutions: ii) Has a unique solution: iii) Has infinite solutions. The attempt at a solution Well, I changed the matrix into reduced...

Ah, NOW I get it. Thanks to everyone for your help!

Alright, I shall try to fix it. (Gotta go, it's time for dinner.) Thanks for your help!

(2sinx)^2*sqrt[4-(2sinx)^2]

Well, I think it's some misunderstanding on my part from the conversion between x and theta. I used the Mathematica online integrator to verify and its answer was: \frac{8}{3} \sqrt{\cos^2 x} \sin^2 x \tan x...which, when I simplify (and perhaps this is the part where I'm wrong), I just end...

The question is: Use x = \tan \theta , \frac{-\pi}{2} < \theta < \frac{\pi}{2} to show that: \int_{0}^{1} \frac{x^3}{\sqrt{x^2+1}} dx =\int_{0}^{\frac{\pi}{4}} \tan^3 \theta \sec \theta d\theta Using that substitution, I got it down to: \int_{0}^{\frac{\pi}{4}} \frac{\tan^3...

The question in my textbook was: \int_{0}^{2} x^2 \sqrt{4-x^2} dx I decided to just leave out the lower and upper limits for now, and just solve \int x^2 \sqrt{4-x^2} dx. (It's a bit long, but I assure you I did the work.) Upon making the substitution of x = 2 \sin \theta, I got it down...

I took your suggestion and worked it out on paper, but...I don't seem to be able to see how this would help. f(x) = (-sec x tan x - tan^2 x)/(sec x + tan x)... I'm afraid I've run into something that's a bit too advanced (this problem was listed under the "challenger" questions..and I was...

Hi, I'm just starting to learn integration (I went to the first class in my summer course yesterday), and I'm already a bit confused. I was doing some practice problems in the text, and I found this: Find the most general antiderivative of f on the indicated interval: f(x) = -\tan x on...