# Triple integral Definition and 16 Discussions

In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in

R

2

{\displaystyle \mathbb {R} ^{2}}
(the real-number plane) are called double integrals, and integrals of a function of three variables over a region in

R

3

{\displaystyle \mathbb {R} ^{3}}
(real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.

View More On Wikipedia.org
1. ### Confused about polar integrals and setting up bounds

So I want to subtract the two surfaces, right? I really don't know where to start... I am guessing this would be some sort of triple integral, however I am very confused with the bounds. Any help would be greatly appreciated! Thanks!!
2. ### Finding center of mass of solid

Homework Statement A solid B occupies the region of space above ##z=0## and between the spheres ##x^2 + y^2 + z^2 = 16## and ##x^2+y^2+(z-1^2) = 1##. The density of B is equal to the distance from its base, which is ##z = 0##. The mass of the solid B is ##\frac{188\pi}{3}##. Find the...

10. ### Finding centroid of a solid

Homework Statement Use cylindrical coordinates to find the centroid of the solid. The solid that is bounded above by the sphere x2 + y2 + z2 = 2 and below by z = x2 + y2 Homework Equations x = rcos(theta) y= rsin(theta)[/B] The Attempt at a Solution I am having trouble trying to find...
11. ### Volume inside a sphere and cone

Find the volume laying inside x^2 + y^2 + z^2 =2z and inside z^2 = x^2 + y^2. This is a problem my professor made, so I have no way of checking my answer. What I did first was completed the square for the sphere and got x^2 + y^2 + (z-1)^2 = 1, which is a sphere of radius one shifted above the...
12. ### Acceleration due to gravity at the centre of a hemisphere

Homework Statement find the acceleration due to gravity at the centre of a solid hemisphere. Homework Equations ##F=\frac{GMm}{r^2}## The Attempt at a Solution i decided to go for cylindrical coordinayes (which is way beyond my syllabus). I did some research though. let me take a point...
13. ### Divergence Theorem Question (Gauss' Law?)

If F(x,y,z) is continuous and for all (x,y,z), show that R3 dot F dV = 0 I have been working on this problem all day, and I'm honestly not sure how to proceed. The hint given on this problem is, "Take Br to be a ball of radius r centered at the origin, apply divergence theorem, and let the...
14. ### Triple Integral of a cone bounded by a plane.

Homework Statement find the volume using spherical coordinates of the region bounded above by z=9 and below by z=sqrt(x^2+y^2) in the first octant. Homework Equations The Attempt at a Solution I found this volume using cartesian and cylindrical coordinates, so I know the answer I am looking...
15. ### Triple Integral, Volume of an Egg

Homework Statement I need to find the volume of an egg with a shape described by: z = 1/2(x2 + y2) and z = 6 - x2 - y2 I am also given that the egg is 6cm in length. Homework Equations I roughly graphed the two surfaces. The first being paraboloid that opens up from the origin, and the...
16. N

### Triple Integral Meaning

Okay so I just have a question on triple integrals. I understand how to use triple integrals to find volumes, but what I really don't understand is what I am really getting when I take the triple integral OF a function. I understand physical examples like taking the triple integral of a...