# All Questions

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### Unitary group as a region

I would like to compute the area of some subspaces of $SU(n)^d$ defined by group equation (basically $U_{i_1}^{e_1}\dots U_{i_k}^{e_k}=1$) . I know that there is the function ...
40 views

### Integrating in regions

I have three rectangles of the same size: ...
89 views

### Converting .STL from Shell to Solid for stress analysis of wing

I'm new to Mathematica as this is the first class I've had to used it in my undergrad time as an aerospace engineer. Anyway, I have run into a problem that I can't figure out. I have created .STL's of ...
99 views

### ImplicitRegion vs DiracDelta [closed]

I've been having troubles with numerical integration over implicit regions, so I checked in a simple example if the result coincides with integrating with a DiracDelta function, and found this rather ...
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### Illustrate homework (integral region with implicit region)

I must integrate: $$\int \int_D x^2y^2 dx dy$$ in the first quadrant. This is a triangle with vertices in $(0,0)$, $(0,1)$ and $(1,0)$. I tried to draw it in mathematica with implicit region: <...
161 views

### Finding the Area and Perimeter

A way to find the region such as the area is using $Integrate[]$, where you take the upper - lower or $f[x]-g[x]$, while the perimeter we add the upper and lower region after we found its arc length. ...
226 views

### Finding an area enclosed by 4 curves

Question is given: Consider the functions $f(x)=x \cos(x)$, $g(x)=-x^3+6$, $h(x)=-10x-50$, $k(x)=sin(x^2/3)+13$. Plot the graphs of the four functions for x in the interval [-8,5]. You should see a ...
344 views

### Finding surface normal for 3D region at a specific point

I would like to find the surface normal for a point on a 3D filled shape in Mathematica. I know how to calculate the normal of a parametric surface using the cross product but this method will not ...
183 views

### How to force a real function to appear with real components [closed]

The command Integrate oftentimes produces output that seems to be a mix of real and complex components even though the result is a real function. The question is ...
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### Mathematica does not respect linearity of integral

Fixed in 11.3 I have the following issue, trying to evaluate an integral. Mathematica tells me ...
588 views

### Area between contours of two surfaces

If I have the two following surfaces: f[x_, y_] := y^3 - x^3 + 3 x^2 - 6 x - 4 y + 4 g[x_, y_] := x^3 + y^3 + x - 2 y - 1 And the two lines defined by the ...
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### Calculate the volume of a 3D List

so I have this set: $B= \{(x,y,z)\mid\mid x\mid\leq2,\mid y \mid\leq 2 ,\mid x*y\mid\leq1, 0\leq z\leq2-\mid x\mid\}$ and I want to calculate the volume, but I have no idea how to define such an ...
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### Drawing and computing area of intersection for implicit regions

I want to visualize in 3d intersecting bodies and compute the volume of their intersection at the same time. It would be very nice if I can rotate 3d view and switch between bodies. If it is too hard ...
76 views

### Computation of volume of a set determined by inequalities

I am beginning Mathematica user. Please help me to solve the following problem with Mathematica - I need to compute value of $$Е=\{2x^7 \le y \le 7 x^7;4y^2 \le z \le 5 y^2;3z^9 \le x \le 8 z^9\}$$ ...
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### Problems with integrating over a region

Following the example of this answer: Find the volume of the region defined by $|x|+|y|+|z|<4$ I tried to compute the following integral over a region by using ImplicitRegion. However, when I ...
609 views

### How to find the area between 3 curves?

I have three equations: $y=3/x$, $y=12x$, and $y=x/12$, $x>0$. I am not sure how to go about integrating an equation once I find the intersections. Do I need multiple integrals?
562 views

### RegionPlot of ImplicitRegion is incorrect

Bug fixed in 10.4. Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect ...
129 views

### When is RegionMeasure[ImplicitRegion[…]] faster than (N)Integrate[Boole[…]]?

I wanted to use Mathematica to compute areas and volumes of various implicitly defined regions, so I ran a simple test case using the unit circle: ...
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### Region bounded by x^2+y^2=1, y=z, x=0, z=0, in first octant

I need to draw (pencil and paper) the region bounded by $x^2+y^2=1$, $y=z$, $x=0$, and $z=0$ in the first octant. So the first assistance I asked of Mathematica is: ...
207 views

### A triple integral involving Abs over an ellipsoidal region

I'm a newbie and I'm trying to calculate a triple integral. But Mathematica doesn't output for half an hour and the CPU occupancy rate of my Wolfram doesn't changed when it's calculating. Here is the ...
1k views

### How to integrate a function of a direction, over the hemisphere

The Mathematica documentation Integrate over Regions gives an example of how to simply integrate over a sphere (surface): Integrate[1, {x, y, z} ∈ Sphere[]] ...
235 views

### Plotting the region bounded by parallel lines

I am working on the integral $$\int\int_D (2x+y)^2 e^{x-y}dA,$$ where $D$ is the region bounded by $2x+y=1$, $2x+y=4$, $x-y=-1$, and $x-y=1$. I need to shade the region bounded by these lines, so I ...
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### Visualize transformation used in multiple integration

In class, we will sketch the region $D$ in $R^2$ bounded by the curves $xy=1$, $xy=4$, $y=x$, and $y=x+2$. Then we will use the change of variables given by $u=xy$ and $v=y-x$. We need to show that ...
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### Old fashioned region method?

Just stumbled across this idea in http://users.rowan.edu/~hassen/Mathematica/Volume%20III/Chapter%2015.pdf. ...
838 views

### Evaluating a surface integral

I'm trying to compute the integral $$\int_S x^2+z^2\,{\rm d}S,$$where $S$ is the surface $$S\colon~ \frac{x^2}{2} + \frac{y^2}{3} + \frac{z^2}{2} = 1, \quad y \geq 0.$$ One possible parametrization ...
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### Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
303 views

### Integration over a (non-parametric) curve defined by indicator function

I want to integrate the real function myFun defined on a 2D plane over the line locus, defined as the solution of a set of ...
730 views

### Finding volume of a segment

I'm still pretty new to Mathematica, so I would like to seek advice regarding a geometrical problem. I am currently trying to define that as an extra condition in the Mathematica code below. ...
365 views

### Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
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 ...