Linked Questions

0
votes
1answer
868 views

Integral over geometric region [duplicate]

I'd like to calculate this integral $$ \int_E y\ dydz $$ where $E = \{ (x,y,z) \in R^3 : z^2+6 < y^2 < 5z \}$ By hand i've got $\frac{1}{12}$ but i'm not sure, and i'd like to verify this ...
18
votes
3answers
5k views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
4
votes
2answers
4k views

Plot3D region bounded by equations?

I have four equations, $$ z = xy \\ z=0 \\ y=x^2 \\ x=y^2$$ I would like to integrate the region bounded by them. Before this, I would like to plot the region they bound, but I cannot seem to find ...
7
votes
1answer
3k views

Calculating volume between two surfaces of revolution

Once again, I'm very new to Mathematica and winging it as I go. I probably don't have the math education at this point to even justify buying it in the first place, but that's off topic. I wanted to ...
3
votes
3answers
171 views

Integrate not restricting variable with Assumptions option?

I am integrating g over the region: ...
3
votes
1answer
410 views

Plot a solid generated by a family of surfaces

I'm trying to graph a series of planes as a solid object in Mathematica. I first tried to use the Plot3D options as well as the fill options to plot a $3D$ volume, ...
1
vote
2answers
946 views

Why Can't Mathematica Integrate this?

I have the following problem from a textbook I am trying to integrate: So, following the directions in text, I am required to integrate each function. However, I cannot get Mathematica to integrate ...
4
votes
1answer
311 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
2
votes
3answers
200 views

Find the solid and it´s volume formed by the intersection of two surfaces

I am trying to plot the solid formed by the intersection of the surface between p1 = Plot3D[1 + x^2 - y^2, {x, -1.2, 1.2}, {y, -1.2, 1.2}] and ...
3
votes
1answer
192 views

Volume under a List3dPlot?

Is there a way to find the volume in cubic feet under a ListPlot3D mesh, in positive and negative regions? I have tried using the Volume command. I created a 3D plot from an excel file of x,y, and z ...