Tagged Questions
3
votes
1answer
180 views
How to calculate the area between 2 polar curves: $r=\frac{4}{2}-\sin\theta$ and $r=3\sin\theta$?
How to calculate the area between 2 polar curves: $r=2-\sin\theta$ and $r=3\sin\theta$?
I know that one curve is a limaçon and the other is a circle. I have them drawn out as well, my only question ...
2
votes
1answer
53 views
evaluation of double order integral using polar co-ordinates
When evaluating double integral using polar co-ordinates,
does the order of $dr ~ d\theta$ make any difference?
Suppose,
$$\int_0^{\pi/4}\int_0^{\sin\theta} r^2 dr d\theta$$
...
1
vote
1answer
63 views
How to calculate a double integral over a triangle by transforming to polair coordinates & by using a transformation
Let T be the triangel with vetrices $( 0,0 ) , ( 1,0 )\mbox{ and } ( 0,1 ) $. Evaluate the integral :
$$
\iint_D e^{\frac{y-x}{y+x}}
$$
a) by transforming to polar coordinates
b) by using the ...
1
vote
0answers
84 views
Explain this limit of integration for radius in polar coordinates.
Use polar coordinates to find the volume of the given solid:
Inside both the cylinder $x^2 + y^2 = 4$ and the ellipsoid $4x^2 + 4y^2 + z^2 = 64$
The limit of integration for the radius goes ...
4
votes
0answers
149 views
Evaluate the integral by converting to polar coordinate
$$ \int^{\pi/2}_{\pi/4} \int^{\sqrt{2-y^2}}_y 3(x-y) dx dy$$
I attempted the following:
$$ \int_{\pi/4}^{\pi/2} \int_{0}^{1} 3r^2 (\cos\theta - \sin\theta) dr d\theta $$
which is wrong apparently. ...
0
votes
1answer
340 views
Numerical Integration of a Gaussian Distribution in Polar Coordinates
I want to numerically evaluate a 2D-integral of a specific probability distribution over some given area (I use MATLAB so all the code below is MATLAB code). I broke down the problem so that it ...
1
vote
2answers
129 views
Length of a plane curve in polar coordinate
Consider the plane curve $\gamma$ in polar coordinates:
$$
r=r_0+e^{\lambda\theta}, \quad \theta_1 \le \theta \le \theta_2,
$$
where $r_0,\lambda,\theta_1>0$. Is it possible to compute explicitly ...
4
votes
3answers
2k views
Simple proof of integration in polar coordinates?
In every example I saw of integration in polar coordinates the
Jacobian determinant is used, not that i have a problem with the Jacobian,
but I wondered if there's a simpler way to show this which ...
2
votes
1answer
149 views
Find volume of a revolved solid by integrating wedges.
So, lets say that I wanted to find the volume of the solid formed by rotating the area between
$f(x)=\sqrt{1-x^2}, 0<x<1$ and the $x$ axis around the $y$ axis. (This example is simply a ...
2
votes
2answers
115 views
Integral variable substitution using Hausdorff measure
Suppose we have positive density $q$ with "good" qualities (continuity, etc..). I need to calculate this integral:
$$\int_B q(\textbf{z}) d \textbf{z},\ \textbf{z} \in \mathbb{R}^d,$$
where $B \subset ...
2
votes
3answers
745 views
Ηοw to find the area of this region
I have two functions $$r=2$$
$$r= 3+2sin\theta$$
and I want to find the area of the yellow region in the picture below.
The limits of the integral solving the equation must be ...
4
votes
2answers
3k views
Why is $dy dx = r dr d \theta$ [duplicate]
Possible Duplicate:
Explain $\iint \mathrm dx\mathrm dy = \iint r \mathrm d\alpha\mathrm dr$
I'm reading the proof of Gaussian integration. When we change to polar coordinates, why do we ...
