All Questions
Tagged with applications integration
14
questions with no upvoted or accepted answers
2
votes
2
answers
106
views
Find the exact length of the parametric curve(Not sure what I'm doing wrong)
As the title says, I'm not sure what I'm doing wrong. Any help would be greatly appreciated. Here's the problem with my solution.
Find the exact length of the parametric curve
$(x,y)=(\theta+\...
- 21
2
votes
0
answers
111
views
Application of integrating $\cos^4 x$?
A student asked a colleague the other day for a practical application that involved needing to integrate the fourth power of cosine, but no one here could think of one off-hand other than some volume ...
- 21
1
vote
0
answers
79
views
Using the trapezoidal rule for the Maxwell-Boltzman function
Background
I approached my physics professor with question 1 from this LibreTexts resource. (at the bottom of the page), to better understand the material via self-study.
Question
Using the Maxwell-...
- 1,426
1
vote
0
answers
57
views
What is the equation and area under curve for Covid load dynamics?
Covid virions on infection, replicate exponentially and once the body's defense system starts attacking it then it also seems to decrease exponentially.
Source
The time period when the PCR test is ...
- 111
1
vote
0
answers
41
views
Sequence of Logic in Diffusion Problem DQ
Problem: If a tank is filled with 100 gallons of water and mistakenly added 300 pounds of salt. To fix the mistake the brine is drained at 3 gallons per minute and replaced with water at the same rate....
1
vote
0
answers
55
views
Change in temperature of overflowing container
This is an integation question, form a Physics context.
Mixing of identical fluids at different temperatures is simple, as per here:
https://physics.stackexchange.com/a/24433/290018
We have a slightly ...
- 111
1
vote
1
answer
686
views
what is the volume generated by rotating the given region.
My professor says the volume generated by rotating the region $\mathscr{R}_2$ about the line $OA$ is $5/\pi$ but I don't see how that could be the answer?
- 107
1
vote
0
answers
58
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Prove that if $V=\text{constant}$ then the second part in the paratheses after the integral sign is equal to $0$
$$\frac{\mathrm d}{\mathrm dt^i} \underset{\large V(t)}{\iiint} \Psi \,\mathrm dV= \underset{\large V(t)}{\iiint} \left({\frac{\partial \Psi}{\partial t}+\nabla\cdot\Psi\mathbf v_i}\right)\, \mathrm ...
- 8,382
0
votes
0
answers
70
views
Arc length vs Surface of revolution.
I don't understand why these two problems are solved differently here the first one $fig(1)$ and 2nd one $fig(2)$. Why did we take the limit $\displaystyle \lim_{r\to0^+}\int_r^\pi \sqrt{2-2cost}\...
user1062191
0
votes
0
answers
101
views
Integral transform with reciprocal complex exponential functions?
I tried answering a question that ended up with an expression
$$\mathcal F\left\{e^{\left(\frac{2\pi j} {t}\right)}\right\}$$
Now this function we know from famous identity is
$$e^{ai} = \cos(a)+i\...
- 26.1k
0
votes
0
answers
296
views
Comparison in the accuracy of Romberg Integration and Second Order Newton-Cotes Quadrature
Context
I ask this question because I'm currently working on a program that solves the Cahn-Hilliard equation in 2D. For this project I need a subroutine to calculate the free energy functional by ...
user594148
0
votes
0
answers
175
views
Riemann-Stieltjes integral $\int\limits_a^b f(x) \, \mathrm{d}g = \frac{\log ^2(n)}{2 \log (10)}|_a^b$
I'm having trouble with this integral:
$\int\limits_a^b f(x) \, \mathrm{d}g = \frac{\log ^2(n)}{2 \log (10)}|_a^b$
If I want to find the product such:
$10^m.10^{m+1}...\leq n$
so for example for $...
- 1,379
0
votes
0
answers
2k
views
Volume enclosed by two spheres (triple integral, cylindrical coordinates)
The question:
Find the volume of the solid enclosed by the sphere $x^2 + y^2 + z^2 -
6z = 0$ , and the hemisphere $x^2 + y^2 + z^2 = 49 , z ≥ 0$
I set up the triple integral
$\int_0^{2\pi}\...
- 11
0
votes
1
answer
63
views
Why can we apply the surface area of revolution theorem to a spiral?
To find the surface area generated by revolving function f which is smooth on the interval [a,b] and $f(y) \ge0$ around the y-axis we can use the formula $$S=\int_a^b 2\pi rdl =\int_a^b 2\pi f(y)\...
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