Recent content by squeeky

That's what I thought at first, but HallsofIvy pointed out that it's actually from 0 to pi. Was I right at first then? Because it does make more sense to me if it is from -pi/2 to pi/2, since I see the limits as lying in the xz-plane.

Ah! That's right, I don't know how I got that cube, I must have been seeing things when I looked up the formula. And so now I get a an equation of \int^{\pi}_0\int^{acos\theta}_0\int^{\sqrt{a^2-r^2}}_{-\sqrt{a^2-r^2}}dzrdrd\theta which (unless I did my math wrong) gives me a somewhat nice...

Homework Statement Use Spherical Coordinates. Let H be a solid hemisphere of radius a whose density at any point is proportional to its distance from the center of the base. a) Find the mass of H. b) Find the center of mass of H. Homework Equations M=\int\int_D\int\delta dV...

Homework Statement Use Cylindrical Coordinates. Find the volume of the solid that the cylinder r=acos\theta cuts out of the sphere of radius a centered at the origin. Homework Equations Sphere = x2+y2+z2=a3 The Attempt at a Solution I think that the limits are from -pi/2 to...

Homework Statement Find the mass and center of mass of the solid bounded by the planes x=0, y=0, z=0, x+y+z=1; density\delta(x,y,z)=y Homework Equations M=\int\int_D\int\delta dV M_{yz}\int\int_D\int x \delta dV;M_{xz}\int\int_D\int y \delta dV;M_{xy}\int\int_D\int z \delta dV...

Homework Statement Use polar coordinates to find the volume bounded by the paraboloids z=3x2+3y2 and z=4-x2-y2Homework Equations The Attempt at a Solution Somehow, through random guessing, I managed to get the right answer, it's just that I don't understand how I got it. Also, because the z is...

I don't know, I still don't get it. I mean yeah I understand the x-limits, it's just the y-limits I'm having problems with. Referring to the original integral, we have the limits of x being greater than y^2 and less than 1, so wouldn't that make the region above the parabola, since it has to be...

Thanks, that solves the problem! Although, I can understand where I went wrong with taking the limits for x, but I still don't quite get why the region is the area outside the parabola, instead of inside.

Homework Statement Evaluate an iterated integral by reversing the order of integration \int^1_0\int^1_{y^2} ysin(x^2)dxdy Homework Equations The Attempt at a Solution I've got that the limits for x is between y^2 and 1, while the limits for y is between 0 and 1. Then I graphed...