# What is Triple integral: Definition and 321 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.

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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. ### Why this triple integral is not null?

Greetings here is my integral Compute the volume of the solid and here is the solution (that I don't agree with) So as you can see they started integrating sinx from 0 to pi and then multiplied everything by two! for me sin(x) is an odd function and it's integral should be 0 over symmetric...
3. ### Problem with a triple integral in cylindrical coordinates

Good day here is the solution J just don't understand why the solution r=√2 has been omitted?? many thanks in advance best regards!
4. ### Is the Triple Integral in Cylindrical Coordinates Correctly Solved?

I am trying to solve it using cylindrical coordinates, but I am not sure whether the my description of region E is correct, whether is the value of r is 2 to 4, or have to evaluate the volume 2 times ( r from 0 to 4 minus r from 0 to 2), and whether is okay to take z from r^2/2 to 8
5. ### I Am I using the right limits on this triple integral?

Let: \begin{align} r&=\sqrt{a^2 + p^2 - 2ap \cos \theta}\\ s&=a\\ t&=p\\ f(r) &= \text{continuous function of } r\\ g(s) &= \text{continuous function of } s\\ \end{align} Consider the expression: \begin{align} \int_{q'}^q \int_{b'}^b g(s)\ \int_{s-t}^{s+t} f(r)\ dr\ ds\ dt\ \end{align} We...
6. ### Represent a 3d region and compute this triple integral

Let ## E=\left\{ (x,y,z) \in R^3 : 1 \leq x^2+y^2+z^2 \leq 4, 3x^2+3y^2-z^2\leq 0, z\geq0 \right\} ## - Represent the region E in 3-dimensions -represent the section of e in (x,z) plane -compute ## \int \frac {y^2} {x^2+y^2} \,dx \,dy \,dz## the domain is a sphere of radius 2 with an inner...
7. ### MHB 15.1.34 Evaluate triple integral

15.1.34 Evaluate $\displaystyle I=\int_{0}^{3\pi/2}\int_{0}^{\pi}\int_{0}^{\sin{x}} \sin{y} \, dz \, dx \, dy$ integrat dz $\displaystyle I=\int _0^{3\pi/2}\int _0^{\pi }\sin(y)\sin (x)\, dxdy$ integrat dx $\displaystyle I=\int _0^{3\pi/2}\sin \left(y\right)\cdot \,2dy$...
8. ### MHB Computing Triple Integral in 'R': A Guide

I would like to compute the triple integral of a function of three variables $f(x,y,z)$in R. I am using the package Cubature, Base, SimplicialCubature and the function adaptIntegrate(), Integrate and adaptIntegrateSimplex(). The integrand is equal to 1 only in certain domain(x<y<z, 0 otherwise)...
9. ### Multivariable Triple Integral - Calculus Physics/Math Problem

Hello everybody. If anyone could help me solve the calculus problem posted below, I would be greatful. Task: Evaluate the moment of inertia with respect to Oz axis of the homogeneous solid A Bounded by area - A: (x^2+y^2+z^2)^2<=zSo far I was able to expand A: [...] so that I receive...

34. ### Where did I go wrong in my setup for this triple integral problem?

Hey guys I've been working some triple integration problems and I've stumbled across a question that I'm having problems with So from the picture below my solution is incorrect and I can't seem to figure out where I went wrong. Is my setup for the integrals correct or is that where I've made my...
35. ### Triple integral forming a solid region

Homework Statement Homework Equations Fubini's theorum The Attempt at a Solution I drawn the diagram with the limits (for x, y, and z) and come up with something with 4 faces, 5 corners, 8 edges is that something you guys got? Thanks
36. ### I Why this triple integral equals zero?

Hello everyone, I have the this inquiry: if I compute de following integral: http://micurso.orgfree.com/Picture1.jpg by numerical methods I get cero as a result. I used Maxima and Mathematica and their functions for numerical integration give me an answer equal to cero. But, if I apply...
37. ### Triple integral in cylindrical coordinates

1. Homework Statement I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong. Homework EquationsThe Attempt at a Solution [/B]
38. ### What is the mass of ceramic on the wire with non-uniform coating?

Homework Statement A metal wire is given a ceramic coating to protect it against heat. The machine that applies the coating does not do so very uniformly. The wire is in the shape of the curve The density of the ceramic on the wire is Use a line integral to calculate the mass of the...
39. ### Triple integral in polar coordinate

Homework Statement why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)? z=p(cosφ) As we can see, φ is not the angle between p and z ... Homework EquationsThe Attempt at a Solution

49. ### Triple integral changing order of integration

Homework Statement rewrite using the order dx dy dz \int_0^2 \int_{2x}^4\int_0^{sqrt(y^2-4x^2)}dz dy dx The Attempt at a Solution I am having trouble because i don't know what the full 3 dimensional region looks like but the part on the xy plane is a triangle bounded by x = 0 , y = 4 and y =...
50. ### Evaluate the triple integral paraboloid

Evaluate the triple integral ∫∫∫E 5x dV, where E is bounded by the paraboloid x = 5y2+ 5z2 and the plane x = 5. My work so far: Since it's a paraboloid, where each cross section parallel to the plane x = 5 is a circle, cylindrical polars is what I used, so my bounds are 5y2+5z2 ≤x ≤ 5 ----->...