Tagged Questions
1
vote
3answers
81 views
Center of Mass of a Circle
How would one find the center of mass of a circle? The center of mass of a rod is given by:
$$\frac{1}{M}\int^{L}_{0}\rho x dx$$
So, for a sphere, it would be an area integral, such as:
...
1
vote
3answers
70 views
Another complex analysis question
I am going to have an analysis exam soon and I found the following question in a past paper:
Evaluate the integral counterclockwise
$$\int |z| \overline{z} \, dz$$
where y is the closed curve ...
1
vote
1answer
90 views
Analysis Exam Questions
I am going to have an analysis exam soon and I found the following question in a past paper:
Evaluate
$$\int \frac{-y \, dx + x \, dy}{x^2+y^2}$$
a) Once counterclockwise around the circle $$x^2 + ...
1
vote
1answer
161 views
Area of a circle
I've tried to find as a personnal exercise where the formula $A=\pi \times R^2$ comes from.
After drawing the problem, I've found that $A = 2\int\limits_{-R}^{R}\sqrt{R^2-t^2}dt$. How can I calculate ...
2
votes
2answers
455 views
subvolume area under the intersection of a plane (line) and a cone
I am implementing a conical filter for Gupta-Sproull anti-aliased line algorithm.
Given a cone with the total volume of 1 and a radius of 1. Find the subvolume of the intersection of a line. The ...
5
votes
4answers
818 views
Calculate $\pi$ precisely using integrals?
This is probably a very stupid question, but I just learned about integrals so I was wondering what happens if we calculate the integral of $\sqrt{1 - x^2}$ from $-1$ to $1$.
We would get the surface ...
