Hello,
I've recently discovered the sine integral and have been playing around with it a bit on some graphing software. I looked at the graph of ##Si(x^2) - \frac π 2## and saw that both the amplitude and period was decreasing as x increased. Curiosity got the best of me so I decided to...
Properly speaking, since sin(x) and cos(x) don't go to zero as x \rightarrow \infty, the following integrals are undefined:
\int_0^{\infty} cos(kx) dk
\int_0^{\infty} sin(kx) dk
However, in the handwavy way of physicists, we can often pretend that the cosine integral "converges" to \delta(x)...
Hello PF,
I just found a curious integral. I wondered if it comes from a bigger group of integral definitions:
\int_0^\infty \mathrm{Si}(ax)e^{-x}\mathrm{d}x=\mathrm{atan}(a)
Where Si(x) is the sine integral function \mathrm{Si}(x)=\int_0^x \frac{\mathrm{sin}x}{x}\mathrm{d}x
I proved the...
Hello, and thanks for welcoming me in the forum of Physics Forums.
I just found a curious integral that I solved by Taylor series. I wondered if it comes from a bigger group of integral definitions:
##\int_0^\infty \mathrm{Si}(ax)e^{-x}\mathrm{d}x=\mathrm{atan}(a)##
Where Si(x) is the sine...
Homework Statement
Solve by variation of parameters:
y" + 3y' + 2y = sinex
Homework Equations
Finding the complimentary yields:
yc = c1e-x + c2e-2x
The Attempt at a Solution
I set up the Wronskians and got:
μ1 = ∫e-2xsin(ex)dx
μ2 = -∫e-xsin(ex)dx
The problem is that I have no idea how to...
This thread will be dedicated to find a general formula for the integral I(a,t) = \int^t_0 x \log|\sin(a x )| \, dx \,\,\,\,\, a,t>0
This is not a tutorial . Any comments or attempts are always be welcomed .
Homework Statement
Any ideas for how to solve the following integral?
$$\int_{0}^{\pi}\sin{n x}\sin{x}^3 dx$$
where n is a positive integer
Homework Equations
Various sine and cosine identities
The Attempt at a Solution
I haven't much of a clue how to solve the integral...
This is not really a homework, I am trying to expand Si(x) into a series.The series expansion of Si(x) is given in articles:
Si(x)=\int_0^x \frac{\sin\theta}{\theta}d\theta=\sum_0^{\infty}\frac {(-1)^k x^{2k+1}}{(2k+1)(2k+1)!}
This is my work, I just cannot get the right answer:
Si(x)=\int_0^x...
Homework Statement
Hi. I need help understanding a task where i am supposed to prove that a function must be greater than 0 when x is from 0 and up. f(x) = (x-0)integral of (sinx/(x+1)) please help me out with this.
Mons
Homework Statement
Si(x)=\int(sint/t)dt from 0 to x
integrand is 1 at t=0
express the solutiony(x) of the initial value problem x^3y'+2x^2y=10sinx, y(0)=0 in terms of Si(x)
Homework Equations
The Attempt at a Solution
y'+2/xy=10x^-3sinx
multiply by x^2
x^2y'+2xy=10x^-2sinx...
Homework Statement
Integral((sin(x))^2((cos(x))^2) dx
Homework Equations
The Attempt at a Solution
Seperate Cos (x)^3
sin(x)^2 (cos(x))(cos(x))^3
Then:apply identities
sin(x)^2(cos(x))(1-sin(x)^2)
And now I am lost!:eek:
Thanks Alot!
i know that the sine integral converges to pi/2. But what about the abs value of the sine integral. It seems to me that it would have value oo. But I'm having trouble coming up with a lower bound that diverges.