# Tagged Questions

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: ...
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 ...
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 + ...
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 ...
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 ...
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 ...