# Tagged Questions

Questions on polar coordinates, a coordinate system where points are represented by their distance from the origin ($r$) and the angle the line joining the point and the origin makes with the positive horizontal axis ($\theta$).

46 views

18 views

22 views

### Cylindrical coordinate derivative of a vector field.

Considering the following identity transformation in cylindrical coordinate: $$\mathbf{v}(R,\theta,z)=R\;\mathbf{e}_{R}+\theta\;\mathbf{e}_{\theta}+z\;\mathbf{e}_{z}$$ Taking its derivative ...
20 views

### How to compute this integrale $\int_{\mathbb R^3} e^{-i\left<x,y\right>} e^{-a\| x\|} \| x\|^{\frac{5}{2} } dx$

I would like to calculate the following integral $$I(a,y)=\int_{\mathbb R^3} e^{-i\left<x,y\right>} e^{-a\| x\|} \| x\|^{\frac{5}{2}} dx, \quad a>0, y\in \mathbb R^3 .$$ Here's what I did: In ...
40 views

### Polar coordinates integration

Compute the following integrals over $R$ $f(x,y)\,dx\,dy$ over the area $R$ where: $f(x, y) = x$ and $R$ is given by $0 ≤ r ≤ \cos θ$ and $f(x, y) = x$. I understand polar coordinates is probably ...
41 views

### World To Screen Game math

I have a Coordinate system, I have my XYZ, pX,pY,pZ and the other player, eX, eY, eZ and I want the Pitch and YAW First the YAW: I first take VectorX = eX - pX VectorZ = eZ - pZ then I ...
14 views

### Hint for setting up this surface integral

$$\iint_S z+x^2y \,\, dS$$ Where S is the part of the cylinder $y^2+z^2=1$ that lies between the planes $x=0$ and $x=3$ in the first octant. I tried to convert to Polar ...
82 views

28 views

### Polar form of generalized superellipse

I am looking for the polar form of the generalized superellipse: $$\left|\frac{x}{a}\right|^{n_2}+\left|\frac{y}{b}\right|^{n_3}=1$$ where $a$ and $b$ are the semi major and semi-minor axes. I have ...
46 views

### Solve the double integral $\int _{-1}^1\int _{-\sqrt{1-4y^2}}^{\sqrt{1-4y^2}}\left(3y^2-2+2yx^2\right)dxdy\:$ [closed]

$$\int _{-1}^1\int _{-\sqrt{1-4y^2}}^{\sqrt{1-4y^2}}\left(3y^2-2+2yx^2\right)\,dx\,dy.$$ I think you need to be solved by the transition to polar coordinates: \begin{cases} x=r\cos(\phi),\\ y=r\sin(\...
I want to find the intersections of pairs of curves in polar coodinates. As an example, I have three circles with different offsets in a plane which you can see here. The offsets are: $\exp\left({\... 1answer 28 views ### Find limits of integral for plane polar co-ordinates question Use plane polar co-ordinates or otherwise to evaluate the integral $$\int\int_D^\ \frac{x^2-y^2}{x^2+y^2} dA$$ where D is the part of the x,y plane bounded by the parabola$y^2=4(1-x)$and the ... 3answers 136 views ### how to integrate this$\int_0^{\infty} r^2 e^{\frac{-r^2}{2}} \, dr$? What am I doing wrong when integrating this? $$\int_0^{\infty} r^2 e^{\frac{-r^2}{2}} \, dr$$ I used integration by parts and set$u=r^2$and$dv=e^{\frac{-r^2}{2}}dr$and I get $$-re^{\frac{-r^2}{2}}... 2answers 121 views ### The function f(r,\theta)=(r\cos\theta,r\sin\theta). Consider the function f:\mathbb{R}^{2}\rightarrow\mathbb{R^2} given by$$f(r,\theta)=(r\cos\theta,r\sin\theta)$$I like to show that f is one-to-one in some neighborhood of any non zero point (r,\... 1answer 27 views ### {\int\int\int}_B dxdydz where B is the region delimited by x²+y²+z² = 4 and x²+y²=3z Take the following integral over the specified region: {\int\int\int}_B dxdydz where B is the region delimited by x²+y²+z² = 4 and x²+y²=3z (i'm answering my own question because I was ... 0answers 23 views ### Integration problem in polar How to integrate double integral$$\int_{0}^{\infty}\!\int_{0}^{2\pi}\ \frac{1}{2}\left(\frac{\partial}{\partial x}-\frac{\partial}{\partial y}\right)g_m \bar{g_n} , d\theta dr$$where$$g_a=(x+... 0answers 36 views ### Ways of representing “half-way” between applying a homeomorphism? Something I am particularly interested in is finding a potential way to create an animation illustrating smoothly how points in one 2D space map to another. In particular, I would like to show ... 0answers 35 views ### Green's Theorem with respect to a given polar region. Using Green's Theorem, compute the counterclockwise circulation$I$of$\vec{F}=\langle-\sqrt{x^2+y^2},\sqrt{x^2+y^2}\rangle$around the region defined by the polar coordinate inequalities$7 \leq ...
Let $D$ be the region in the xy-plane bounded on the left by the line $x=2$ and on the right by the circle $x^2 + y^2 = 16$. Evaluate $$\iint (x^2 + y^2)^{-3/2}dA$$