All Questions
Tagged with applications integration
63
questions
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 ...
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
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
3
votes
2
answers
295
views
Can we clarify this "accumulated money flow" application of integration?
I read about this model/application in Calculus with Applications, 11th Edition by Lial, Greenwell, and Ritchey (example), where if you have a function $f(t)$ that models some revenue stream, the rate ...
- 19k
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
3
votes
1
answer
183
views
How to get the integral of $\log(\det(A + Bt))$ w.r.t variable t?
Suppose we have two positive definite matrices $A$ and $B$, now I want to get the integral of:
\begin{align}
\int_{a}^{b} \log(\det(A + Bt)) dt ~~~~~~~~~~~~\text{for } a, b > 0
\end{align}
...
- 123
3
votes
1
answer
320
views
Applied calculus problem
This has been returned as homework and I have to make corrections. My teacher isn't very helpful and I can't afford a tutor.
When satellites circle closely around a planet or moon, the gravitational ...
- 200
3
votes
1
answer
400
views
Domains of Integration -- the kernel trick and box-muller
I wonder if there is any deeper connection between two "tricks" from applied math, the kernel trick and the box-muller algorithm for generating draws from a random normal.
The kernel trick, used in ...
- 4,602
2
votes
2
answers
2k
views
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{...
- 1,927
2
votes
2
answers
282
views
Find the area bounded by $x=-y^2$ and $y=x+2$.
Question
Find the area bounded by $x=-y^2$ and $y=x+2$.
My Attempt
I know it is a very simple question to ask on MSE, but I don't know why I get stuck.
If you trace the graph, then the point of ...
- 772
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
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
2
answers
225
views
Volume of a circle $x^2 +y^2 \leq 1$ which is revolving around a line $x+y=2$.
I want to compute the volume of a circle $x^2 +y^2 \leq 1$ which is revolving around a line $x+y=2$. Usually I solved problems about solids revolving around axis and non axis horizontal and vertical ...
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