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22 views

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 ...
1
vote
1answer
40 views

Integrating in regions

I have three rectangles of the same size: ...
1
vote
1answer
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 ...
0
votes
1answer
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 ...
5
votes
4answers
291 views

Computing surface integral on the unit sphere

I have a function $f$ which takes three unit vectors of $\mathbb R^3$ and returns a number, so $f \colon \mathbb R^3 \times \mathbb R^3 \times \mathbb R^3 \to \mathbb R$ which is defined as $f(\...
1
vote
1answer
99 views

Supposedly same integral gives different results

I need to compute the number $ \sigma_U $ for every open bounded subset of $ n $-dimensional Euclidean space defined as $$ \sigma_U=\iint_Ud(x,y)\mathrm dx\mathrm dy $$ How can I compute this? For $...
2
votes
2answers
87 views

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: <...
2
votes
2answers
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. ...
5
votes
2answers
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 ...
5
votes
3answers
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 ...
4
votes
1answer
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 ...
3
votes
2answers
250 views

Solid of revolution generated with two curves

I'm trying to get the solid of revolution that is generated with two implied curves.The problem say,find the volume of the solid obtained by rotating the region bounded by the curves $x=3y^2-2$ and $x=...
6
votes
3answers
496 views

Area of x^2 + y with {x, y} ∈ ImplicitRegion[x^2 + y^2 < 2, {x, y}]

I want to get the area of the set $\{x^2 + y\, | \,x^2 + y^2 < 2\}$, meaning I want to get the area of the surface defined by $\qquad f(x,y) = x^2 + y$ with the domain given by $x^2 + y^2 < ...
19
votes
1answer
293 views

Mathematica does not respect linearity of integral

Fixed in 11.3 I have the following issue, trying to evaluate an integral. Mathematica tells me ...
6
votes
3answers
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 ...
0
votes
0answers
26 views

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 ...
0
votes
0answers
39 views

Integrating the series representation of a function over a “Polygon” region

I have some function $u(x,y)$ which I'm representing using a series expansion, and I'm trying to integrate $u(x,y)\frac{\partial u(x,y)}{\partial x}$ over a diamond shaped area with coordinates $(0,-\...
3
votes
0answers
75 views

Extract explicit region (integration bounds) from ImplicitRegion

Using an ImplicitRegion in NIntegrate by far best performance is obtained by using ...
1
vote
2answers
305 views

Integrating over Implicit Regions with unspecified parameter

So have this code (giving the moment of inertia of a cube) ...
4
votes
3answers
101 views

Using logical combinations for regions

I'm studying something through the video Volume of Surface of Revolution. To be more exact, from the time 26:22 ... I was able to define the analysis section: ...
11
votes
2answers
1k views

Center of mass of 2D region

The problem states: Find the center of mass of a thin plate covering the region between the​ x-axis and the curve $$y=20/x^2, 5 \leq x \leq8$$ if the​ plate's density at a point​ (x,y) is $\delta(x)=...
0
votes
1answer
165 views

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 ...
0
votes
2answers
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 $$Е=\{2x^7 \le y \le 7 x^7;4y^2 \le z \le 5 y^2;3z^9 \le x \le 8 z^9\}$$ ...
4
votes
1answer
402 views

Another Volume by ImplicitRegion and RegionPlot3D question

I'm still struggling with RegionPlot3D. I need to find the volume of the solid generated by rotating the region bounded by $x=y^4+1$, $y=0$, and $x=2$ about the $y$-axis, the exact answer of which is $...
5
votes
1answer
313 views

How can I find the point in a list of points that is nearest to a given point? [duplicate]

I have a function $f(x)=\{\sin(x),\cos(x)\}$, $\,x=\{0,0.01,...,1\},$ and a point $P=\{2,3\}$. I want to find the $x_0$ such that the distance between $P$ and $f(x_0)$ is minimum. My code is: ...
1
vote
1answer
220 views

integral over a region boundary

I want to integrate a complex function over a boundary of a region: $$-\frac{i}{v}\oint_\Gamma \exp(-2\pi i(ux+vy))\,dx,$$ where $\Gamma$ is the closed boundary of a region and $y = f(x)$. I know ...
7
votes
2answers
500 views

Area of a loop of a curve in polar coordinates

With the curve of equation $r^{n}=a^{n}\cos n\theta$ the area of one of its $n$ loops is $$\frac{a^{2}\sqrt{\pi }}{2}~\frac{\Gamma (\frac{1}{2}+\frac{1}{n})}{\Gamma (\frac{1}{n})}$$ This can be ...
7
votes
1answer
198 views

Calculating second moment of inertia for a region

Let's say I want to calculate the moment of inertia of a half circle around its centroid. I set up a function to calculate the inertial moment like so: ...
3
votes
1answer
771 views

Plotting the 3D region that determines a volume

I need to plot this with Mathematica: Use a triple integral to determine the volume of the region below $z = 4 - x\,y$ and above the region in the xy-plane defined by $0 \leq x \leq2,\ 0 \leq y \...
3
votes
2answers
170 views

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 ...
3
votes
2answers
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?
6
votes
2answers
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 ...
9
votes
1answer
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: ...
9
votes
4answers
3k views

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: ...
3
votes
1answer
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 ...
1
vote
2answers
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[]] ...
4
votes
3answers
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 ...
5
votes
1answer
215 views

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 ...
7
votes
1answer
184 views

Old fashioned region method?

Just stumbled across this idea in http://users.rowan.edu/~hassen/Mathematica/Volume%20III/Chapter%2015.pdf. ...
3
votes
1answer
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 ...
7
votes
1answer
245 views

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 ...
1
vote
2answers
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 ...
8
votes
3answers
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. ...
0
votes
1answer
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, ...
0
votes
1answer
846 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 ...
1
vote
2answers
113 views

Unknown limit of an array of area integrals

Could someone explain why Mathematica can't finish computing this limit (this is a limit of an array, when n -> Infinity (n ...