# Tagged Questions

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### How is taking the average of an integral over an interval justified?

I have been studying classical mechanics and often when going through a worked problem I see a step where there is an integral from 0 to 2$\pi$ of $\sin^{2} \theta \ d\theta$. Instead of using the ...
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### Electric Flux. Integral of $E$ with respect to $A$ is equal to TOTAL Electric FLUX? [on hold]

The first equality is simple to me but I don't understand the second one,$\oint {\bf E}\cdot d{\bf A}$. And the second second last line is much hard to understand. Could you please give some lecture ...
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### A basic math identity often used in integrals

I'm just wondering about why $y_i=A_{ij}x_j$ implies $$d^Ny=(\det A)d^Nx.$$ I see that $\det A$ is the product of the eigenvalues of a diagonal matrix but still don't exactly see how. Please help.
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### Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
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### Integration of 3-momentum

During a lecture that I missed, I was trapped when the lecturer uses the relation $$dp_x~ dp_y ~dp_z ~=~d^3\mathbf{p} ~=~ 4\pi p^2 dp.$$ Can I know how is this relation derived please?
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### Average velocity = Arithmetic Mean

I am having trouble grasping how the average velocity of a particle between an initial position and final position equals to the arithmetic mean of the initial velocity and the final velocity when the ...
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### I reached a result concerning displacement with quantized time intervals. Am I on to something?

A few days ago, I realized a similarity between distance with constant acceleration, $d = v_i t + 1/2 a t^2$, and the sum of integers up to n, $(n^2 + n)/2$. This came up again today when I decided to ...
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### Nicholas Kollerstrom article on the history of Calculus

Today, Newton´s birthday, I read an article posted in the arXiv by Nicholas Kollerstrom http://www.arxiv.org/abs/1212.2666 That basically claims that Newton did not invent Calculus. The article does ...