All Questions
11
questions
1
vote
0
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79
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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
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
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 $$S=\int_a^b 2\pi rdl =\int_a^b 2\pi f(y)\...
- 318
1
vote
2
answers
538
views
When can I apply the trapezoidal rule?
An artificial lake has the shape illustrated below , with adjacent measurements 20 feet apart. Use suitable numerical method to estimate the surface area of the lake.
I know how to solve this problem ...
- 318
4
votes
1
answer
387
views
I've never been so confused (Application of Integral Calculus)
Here's a problem on Application of Integral calculus to find the work done in moving a particle. I was able to 'reach' the 'right answer'. But I'm totally confused and utterly dissatisfied with the ...
- 1,156
1
vote
1
answer
90
views
Why $\int_0^h 2 \pi \frac{rx}{h} \, dx \neq \pi rl$
I'm new to calculus.
I saw a proof for volume of cone using integral. They taken the cone's vertex at $(0,0,0)$, it's base centre at $(h,0,0)$ and it's radius is $r$
$$V=\int_0^h \pi \left(\frac{rx}{h}...
- 15
3
votes
5
answers
110
views
Finding the area bounded by $y = 2 {x} - {x}^2 $ and straight line $ y = - {x}$
$$
y =\ 2\ {x} - {x}^2
$$
$$
y =\ -{x}
$$
According to me , the area
$$
\int_{0}^{2}{2x\ -\ { x} ^2}\, dx \ + \int_{2}^{3}{\ {x} ^2\ -\ 2{x} }\, dx \\
$$
Which gives the area $ \frac{8}{3}$
But ...
user589548
0
votes
1
answer
4k
views
UNRESOLVED: Pushing oil out of a tank using work integration
I have a tank of oil with a density of $900\frac{kg}{m^3}$. My tank has a spout that is $2$ meters tall and the general radius of the tank is $6$ meters. It is half full of oil and I want to find the ...
- 575
0
votes
1
answer
2k
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How can I write the radius equation for the disk method if the axis of revolution intersects the area between the curves
A specific example would be revolving the area between $x^2-5$ and $5x$ below the $x$-axis about $y=-2$
PS - in general, I am assuming that revolving about any other horizontal or vertical line ...
- 391
6
votes
1
answer
2k
views
Volume vs. Surface Area Integrals
In order to find the volume of a sphere radiud $R$, one way is to slice it up into a stack of thin, concentric disks, perpendicular to the $z$-axis. a disk at any point $z$ will have radius $r=\sqrt{R^...
- 16.6k
3
votes
2
answers
5k
views
Interpretation of definite integrals [closed]
It is known from the Fundamental Theorem of Calculus that
$$\int_a^b f(x)=F(b)-F(a).$$
This has the geometric interpretation of the net area between $f(x)$ and the $x-$axis. I suspect that there are ...
- 5,616