All Questions
Tagged with applications integration
64
questions
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Can you help me for prove this Elzaki transform? [closed]
a) proof
$$ E[tf'(t)]=v^2 \frac{d}{dv} [\frac{T(v)}{v}-vf(0)]-v[\frac{T(v)}{v}-vf(0)]$$
Using Elzaki transform
$$E[tf'(t)]=v^2 \frac{d}{dv} [E(f'(t))]-vE(f'(t)) $$
using$$ E[f'(t)]=\frac{T(v)}{v}-vf(...
0
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1
answer
39
views
How to solve an ODE where the rate is directly proportional to two amounts?
Two chemicals in solution react together to form a compound: one unit of compound is formed from $a$ units of chemical $A$ and $b$ units of chemical $B$, with $a + b = 1$. Assume the concentration ...
- 4,450
1
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0
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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
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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
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0
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41
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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....
0
votes
0
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70
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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
1
answer
63
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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)\...
- 318
1
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2
answers
537
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When can I apply the trapezoidal rule?
An artificial lake has the shape illustrated below , with adjacent measurements 20 feet apart. Use suitable numerical method to estimate the surface area of the lake.
I know how to solve this problem ...
- 318
1
vote
1
answer
61
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Why can we say here that $\Delta x_i=dx$ as $i$ approaches infinity?
In the proof of the arc length formula we assume that an element of the arc length is $$\Delta L_i=\sqrt{(\Delta x_i)^2+(\Delta y_i)^2}=\sqrt{1+\left(\frac{\Delta y_i}{\Delta x_i}\right)^2}\space \...
user1062191
1
vote
1
answer
50
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Calculus application question
My attempt:
Step 1: Find $x$ in terms of $t$.
$\frac{dt}{dx} = \frac{1}{-0.15x}$
$t = \frac{1}{-0.15}\ln(x) = x^{-1}(t)$
$x(t) = e^{-0.15t}+c$
However, here is where I am stuck. Without any extra ...
- 1,190
1
vote
1
answer
298
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Using integration to find the population $x$ after a time $t$ years. Having a problem with getting a negative log input.
I'm a little bit confused by a question I came across. It says:
If there were no emigration the population $x$ of a county would increase at a rate of $2.5 \%$ per annum.
By emigration a county loses ...
- 71
4
votes
1
answer
387
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I've never been so confused (Application of Integral Calculus)
Here's a problem on Application of Integral calculus to find the work done in moving a particle. I was able to 'reach' the 'right answer'. But I'm totally confused and utterly dissatisfied with the ...
- 1,156
0
votes
2
answers
2k
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Work on a chain (applications of the integral)
A 10-foot-long chain weighs 25 lbs. And hangs from a ceiling. Calculate the work done in raising the lower end of the chain to the ceiling so that it is at the same level as the upper end.
Please, ...
0
votes
1
answer
100
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Calculus applications - oil leaking from a boat
So here is the question:
The fuel from a ship leaks into the sea forming a circular oil slick. The area of this circle is increasing at the rate of $20$ $m^2$ per minute.
They asked me to prove that ...
- 1,190
2
votes
2
answers
2k
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Line $y = mx$ through the origin that divides the area between the parabola $y = x-x^2$ and the x axis into two equal regions.
There is a line $y = mx$ through the origin that divides the area between the parabola $y = x-x^2$ and the x axis into two equal regions. Find m.
My solution:
When I compute my answer, I get $1-\frac{...
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