This concern all problem requesting techniques and tricks about changes of variables in both computation of limits and integrals
Questions tagged [change-of-variable]
1125 questions
0
votes
3 answers
Tricky triangle with variables question
In the right-angled triangle (ABC), the height divides CD and the hypotenuse AB in the ratio 3:2. Calculate the relationship between height and hypotenuse exactly, as simple as possible.
Iggy
- 5
0
votes
1 answer
instantaneous rate of growth
Populations of two species $A$ and $B$ at time $0$ are equal. If the
instantaneous rates of growth of populations of species $A$ and $B$
are $u$ and $u + 1$ respectively, $u > 0$, then at time $1$ the
population of species $B$ would be
(a)…
onelessproblem
- 383
0
votes
2 answers
Finding original region after change of variables integral calculus
Let us consider the mapping $\phi:\mathbb{R}\to\mathbb{R}$ given $\phi(u,v):\begin{cases}
x=u+v\\y=v-u^2
\end{cases}$
Let $D$ denote the triangle with vertices $(0,0),\,(2,0)$ and $(0,2)$ in the plane $(u,v)$. Show that $\phi$ is a change of…
Heav
- 1
0
votes
1 answer
How to get from $\frac{1}{2\pi}\frac{e^{jn}-e^{-jn}}{jn}$ to $\frac{1}{2\pi}\int\limits_{-1}^{1}e^{j\omega n} d \omega$?
How to get from:
$$\frac{1}{2\pi}\frac{e^{jn}-e^{-jn}}{jn}$$
to:
$$\frac{1}{2\pi}\int\limits_{-1}^{1}e^{j\omega n} d \omega$$
as given here:
https://dsp.stackexchange.com/a/38854/16003
mavavilj
- 7,270
0
votes
1 answer
Choosing a change of variable
I need to choose a fitting change of variable to evaluate this integral:
$$\phi=\phi_0 \mp \int^u du \left( \frac{2mE}{l^2} + \frac{2m^2\gamma u}{l^2}-u^2 \right)^{-1/2}$$
Is there any clever way of knowing what would be a good change of variable in…
Nana
- 43
0
votes
2 answers
How do I perform a change of variables?
Use a change of variables to evaluate:
$$\iiint\limits_{D}xy\,\mathrm{d}V$$$D$ is bounded by the planes $y-x=0$, $y-x=4$, $z-y=0$, $z-y=1$, $z=0$, $z=5$.
A similar question was asked here. It was never answered, because the OP demonstrated that…
pseudoeuclidean
- 1,012