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Dec
15
comment How to calculate$ \int_0^{\infty} e^{-x^2} \sin x dx$ in the most simple way
@Lucian: My comment is not as useful as I thought it would be. It would work if the limits were $\pm \infty$ (of course, the integral would be zero), but it doesn't work here because after completing the square, the limits of integration are not simple. It does let you get to the Dawson function quickly, but I thought you could get a closed form solution.
Dec
15
comment How to calculate$ \int_0^{\infty} e^{-x^2} \sin x dx$ in the most simple way
Use $\sin x = (e^{ix}-e^{-ix})/2$.
Nov
13
comment Does the matrix exponential take open sets into open sets?
@m.g.: Well, that was simple. You should post that as an answer.
Nov
13
comment Does the matrix exponential take open sets into open sets?
@Jack: what about $x^2$ on $(-1,1)$?
Oct
8
comment How do I take the limit of this function?
You must be doing something wrong: when I put in $2.1$, $2.01$, $2.001$, I get $15$, $150$, $1500$, etc.
Jun
16
comment Using dimensional analysis to evaluate $\frac{d}{dx}x^n$
@tpb261: I feel like the issue here, this being a man site and all, is showing that you can't make a non-constant dimensionless function out of only $ x $. For all we know, there might be a constant $ a $ with dimensions of length such that $ c =x/a $.
Jun
16
comment I can't quite figure out this “separable equation”
Small correction: having $\ln x$ in the equation already tells us that $x \neq 0$. Instead, you should assume that $x \neq 1$ so $\ln x \neq 0$.
Jun
16
comment Using dimensional analysis to evaluate $\frac{d}{dx}x^n$
I'm wondering if this would be a better fit at Physics, or if they would tell you that it's obviously correct.
Jun
7
comment How to explain the perpendicularity of two lines to a High School student?
The question is about how to explain the fact that the product of the slopes is $-1$.
Jun
7
comment How to explain the perpendicularity of two lines to a High School student?
I think you should read the question a little more. A high school student doesn't need real life examples to understand what "perpendicular" is.
Apr
27
comment Have you encountered this integral?
I think you mean $P$ is the transform of $f$.
Apr
23
comment Taylor expansion of a not easily differentiable function
@Fred: Taylor series around where? The function doesn't work for $ x\le 1$, that's the problem.
Apr
13
comment Difficult Improper Integral
What's so terrible about $\frac{114}{19}$?
Feb
6
comment For which constants does the following converge to a delta function?
Depending on your definition of a delta function this may not be possible, since the integral of your function over $\mathbb{R}^2$ doesn't converge for any $n$, no matter what $c_n$ is. As far as I know, the delta function must verify $\int_\mathbb{R} \delta(x)\ dx = 1$.
Feb
5
comment Evaluating $\int \frac{1}{\sqrt{x^2 + a^2}}\, dx$ without resorting to trigonometric $u$-substitution
Would you accept hyperbolic functions? :)
Jan
1
comment Is this a solution to the indefinite integral of $e^{-x^2}$?
This is a nice idea, but I'm sorry to tell you that there's proof that there is no elementary formula for the integral. If you're okay with a series, just expand $ e^{-x^2} $ and integrate term by term.
Dec
13
comment Can integration get the real value of $\pi$?
@user3015600: You could, in principle, get $\pi$ with infinite precision. If you want any digit of the decimal expansion of $\pi$, there's a zillion formulas that you can use to get it. The problem is that we can never know all of them, not because math doesn't work, but simply because there's infinitely many of them and we don't have infinite time.
Dec
10
comment Explain complex numbers
Also, I think this is a duplicate: math.stackexchange.com/questions/251665/…
Dec
10
comment Explain complex numbers
@tandberg: You can't always explain something at a level the other person can understand. If your cousin is familiar with the plane and a bit of analytic geometry, you can make the connection there. Otherwise, I'm not sure.
Nov
25
comment $2\times2$ matrices are not big enough
@MarcvanLeeuwen: The reason I made my comment is that yours seemed to imply that this isn't a very good example because it's not evident how to define a rotation matrix for $n > 2$ dimensions. I just wanted to make clear that $3$-dimensional rotation matrices are easy to define and don't commute, that's all.