All Questions
Tagged with applications integration
63
questions
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
1
vote
0
answers
58
views
Prove that if $V=\text{constant}$ then the second part in the paratheses after the integral sign is equal to $0$
$$\frac{\mathrm d}{\mathrm dt^i} \underset{\large V(t)}{\iiint} \Psi \,\mathrm dV= \underset{\large V(t)}{\iiint} \left({\frac{\partial \Psi}{\partial t}+\nabla\cdot\Psi\mathbf v_i}\right)\, \mathrm ...
- 8,382
0
votes
1
answer
375
views
Area under a basketball shot
The other day, someone asked me how to find the area under a basketball shot. It looked something like this:
How would I go about doing this?
user319034
2
votes
1
answer
4k
views
Area bounded by$ y^2=x^2(1-x^2)$
Find the area bounded by $y^2=x^2(1-x^2)$?
I think in this way as the graph lies between -1 to 1 the area is 4 times of $\int x \sqrt{1-x^2} dx$ limits from 0 to 1. Am I correct?
- 1,144
1
vote
1
answer
246
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Work problem - chain hanging on the ground
I am a bit tripped up on the following work problem --
A 30 ft long chain is hanging from one end on a hook, 25 feet above the ground; naturally, this means 5 feet of the hook are on the ground ...
- 165
1
vote
4
answers
2k
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What is the exact role of the integrals in a PID Controller?
I am trying to understand the function of a PID Controller.
It returns a value, which is the sum of three components. The proportional, derivative and integral components. I am having issues grasping ...
- 7,211
2
votes
4
answers
1k
views
How does Volume work with integration?
Using a cross section suppose, as described here: Area formula Paul Notes
Suppose this is: $y = f(x)$.
He says the volume is:
$$\int_{a}^{b} A(x) dx$$
But how does area over that interval give ...
- 11.2k
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
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
0
votes
0
answers
2k
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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
52
views
Finding the work using integrals
A tank full of water has the shape obtained by revolving the curve $y = arcsin(x)$ around the y axis
from $x = 0$ to $x = 1$. Find the work required to pump the water out of the tank. (The density of ...
- 25
0
votes
2
answers
963
views
"Present value and accumulated value of money flow" problem
Find the present value and accumulated value after 10 years for an income stream with the rate of money flow $f(t) = 200 + 150t$ dollars per year and the rate of interest 12% compounded continuously. ...
- 2,062
1
vote
1
answer
3k
views
Optimisation of a rectangles area under a function curve
I have a questions asking for the dimensions of the rectangle with the largest area that has two bottom corners on the x axis and two top corners on the curve $y=12-x^2$.
I have plotted the curve and ...
- 507
6
votes
2
answers
999
views
Applications of integrals of rational functions of sine and cosine
I earlier asked this question about conformal equivalence of flat tori with embedded tori.
In the ensuing thread the integral $\displaystyle\int\frac{dx}{R+\cos x}$ occurred. If I'm not mistaken, it ...
1
vote
1
answer
2k
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Engineering Application with Integration
(source: gyazo.com)
I need help for part $(i)$ ... What I think I know so far:
$P = dgh = (1000)(9.8)(h)$
Finding $h$:
We will choose an arbitrary value '$x$' somewhere between $0$ and $3$.
The ...
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