Recent content by Sombra

Last week (or longer) I asked how to integrate the following rotated 360 degrees about the x-axis (and I still can't figure it out): y= [(1-(x-3)^2)/9)]^(1/2) + 2 When I applied the boundaries of 0 to 6, I got 23.2 cm^3, but I don't think its the boundaries that are my problem, I think it...

ok, so I ended up figuring out the first and last terms without substitution, but I'm using it for the middle one. I sad let u= x-3 and then du/dx= 1 so du=dx. But in order to do that, I think I still need to have the derivitive of 1-u^2 in order to apply the rule, which would be 2u, but how can...

By the way, if you get a nonreal answer for this like I did on the calculator, this problem is part of my bigger problem of finding the volume of the ellipse: y = ((1-(x-3)^2)/9)-2, which is supposed to have its center at 3, cross the x-axis at 0 and 6, and have a maximum y value at 2, rotated...

I'm trying to integrate this awful expression (by dx): {[1-(x-3)^2]/9 - 4[(1-(x-3)^2)/9)^1/2] + 4 Help! How can I integrate this? It's so complicated. For the first part, would it be [x- (x-3)^3]/27x? For the last one I know it is 4x, so that's not a problem, but its mainly the second term...

So, for the first one, the answer would be 4pi, correct? For the second one, I thought the 2 functions interesected at (1,3), so I said the volume was pi times integral (with boundaries of 0 and 1) of [(4-x^2) -(3x)] dx since it has to be subracted. But I think I need to find the integral of...

if I want to find the volume of y= (x + 2) ^(1/2) about the x-axis with the boundaries of -1 and 1, then would it be : V = pi times integral of (x+2) dx?? Its confusing trying to set it up. The volume of a section would be v = pi r^2 (delta x) Also I'm having trouble finding the volume of...

Thanks. For the second part, something like l 3x-4 l >5

If I have a problem such as x^2 + 3x <10 and I got -5 and 2 as my answers, would it be x< -5 and x<2? or -5<x<2?? and when there is an absolute value symbol in the problem, when finding the other answer, do I flip the inequality sign? Please help me remember the rules on inequality!

hmmm I got 5. That seems to work. Thanks!

ok, I got the 1st one. For the second one, I did have the sign right, I just typed it wrong here. I still end up with an irrational quadratic equation.

I need a little help. Could someone get me started (or tell me what's wrong with what I have)? 1. Show that if y = x^(-1/2), x>o, then y' + y/2x = 0 First I found the derivitive of y, which came to be -1/2 x^(-3/2). Then I added it to y/2x, and substituted the value of y in terms of x, but...

Yeah, for number 1, I understand, I just didn't think that sin^2 + cos^2 was 1. For the second one, how do you know that the limits change and what they change to. And for the last, the denominator is not under the radical sign.

1. Why does the derivitive of y= (cos^2(x) + sin^2(x))^6 equal 0? I don't see how it turns out that way. 2. Why does the integral of (1/(x+3)^3 with the lower boundary 2 and upper 5 equal 39/3200? 3. Finally, I don't understand how to integrate: [sq rt(ln x)/x] because I can't figure out...

Physics Questions (mult choice!) These questions confuse me: 1. A heat engine operates in a Carnot cycle b/w two reservoirs, a hot reservoir at temperature T(h) and a cold reservoir at T(c). The efficiency of the engine is 50%. The temperature of the hot reservoir is increased to 2T(h). The...

Now I am totally lost... I know I have to integrate only the top half of this loop and multiply it by 2 to find the area or it will equal 0. I just do not know how to set up the problem to make it only the top half of the loop.