Triple integral Definition and 316 Threads

Hi, I don't know whether this is the best place to ask, anyway, I would like to check my results in Maple and don't know how to evaluate something like this there: \iiint_{M} z^2\ dx\ dy\ dz\mbox{ , where M = [x,y,z] \in \mathbb{R}^3, x^2+y^2+z^2 \leq R^2, x^2 + y^2 + z^2 \leq 2Rz} There is...

Hello. This is my first of many posts at this forum. For fun recently I came across a triple integral that i would really like to know how to do. basically i have two equations x^2+y^2+z^2=1 x^2+y^2+(z-1)^2=2 if you plot these you will see that they intercept. i need to find the area...

"Suppose that a smooth vector field F(x,y,z) given on a region D has the property that on the bounding surface S it is perpenticular to the surface. Show that \int\int\int_D \bigtriangledown \times F dV = 0 in the sense that each component of \bigtriangledown \times F has integral 0 over D."...

Hi, Please can someone help me with this problem: find the triple integral over T( using spherical coordinate) T: 0<=x<=1 0<= y<=sqrt(1-x^2) sqrt(x^2+y^2)<= z <= sqrt(2-(X^2+y^2)) please help me just to find the boundaries of the integrals. I tried but I did not find the...

Evaluate the triple integral \int \int \int xy*DV where E is the solid tetrahedon with vertices (0,0,0), (4,0,0),(0,1,0),(0,0,7) first I'm going to find n: AB= <-4,1,0> AC= <-4,0,7> AB X AC = <7,28,4> = n so i get this equation: 7(x-4) + 28y + 4z = 0 => 7x+28y+4z = 28 so the...

Firstly, can someone please demonstrate the proper Latex code for the terminals on a multiple integral? Thanks! Anyway, as you can probably see, I'm calculating the volume enclosed by x^2+y^2+z^2 = 2 and z = x^2+y^2 using a change to cylindrical coordinates. V =...

I'm having trouble with evaluating [Triple Integral] |xyz| dx dy dz over the region (x/a)^2 + (y/b)^2 + (z/c)^2 <= 1 Do I need to use some sort of parametrisation for the region, and is there some way of dealing with the absolute value function without integrating over the eight...

ok, so I've got this triple integral: \int_{0}^{2} \int_{0}^{y^3} \int_{0}^{y^2} f(x,y,z) dz\, dx\, dy\ what i want to do is get the other five integrals that are equivalen. I've got correctly 3 of them, but, for the life of me, cannot get dy dz dx and dy dx dz to work out. i've...

The problem says to find the volume of material cut from the solid sphere, r^2 + z^2 \le 9 by the cylinder, r = 3\sin\theta I don't know how to graph the first equation, but I can do the second in polar coordinates. How do I go about converting to use cylindrical coordinates?

Triple Integral setup... \int \int \int_{G} 6x (z+y^3) dx dy dz G bounded by x = 0, \ x = y, \ z = y-y^2, \mbox{and} \ z=y^2 - y^3 x from 0 to1 y from 0 to x z from z=y-y^2 to y^2 - y^3 and the integration order becomes dz dy dx would this give the right answer? what aboiut this...

Ok I hve a triple integral problem for find the area of the following: cylinder: x^2 + y^2 = 4 plane: z = 0 plane: x + z = 3 It is a cylinder cut at the xy-plane and by the last plane. It looks like a circular wedge standing straight up from the xy-plane. I just can't figure out...

A cone of height h and base radius r has density equal to distance from its base. Find it's center of mass. How do I write a function for the density? Is it p=h-z? And what are the limits of r if I want to do this in cylindrical coordinates? Thanks in adv.

\iiint {\sqrt(R^2 - 2aR\cos\theta + a^2)} R^2 \sin\theta\,dR\,d\theta\,d\phi with the integration over R between 0 and a the integration over between 0 and pi the integration over between 0 and 2pi Should I use integration by parts or should I take the R^2 sin(theta) under the square...

I have a group of problems that deals with the equations: f(x,y)= x^2+y^2 g(x,y)=20-(x-4)^2-(y+2)^2. I know that the surfaces z=f(x,y) and z=g(x,y) intersect in a closed curve, C, and the projection of C onto the xy-plane is a circle. However, I am having trouble finding its...

I have a hemispherical surface of radius R with it's base centred on the origin. We are using the convention: r is the radius i.e. the magnitude of the position vector of a point: its distance from the origin. theta is the polar angle phi is the azimuthal angle I am asked to...

Hello. Here is the original question http:// My difficuly is understanding the limits of integration--- party due to how the solid in question is "sliced" by those planes. I know how to visualize the parabolic cylinder, but I need help on 1. limits on integration, and 2. Order of...