# What is Dx: Definition and 306 Discussions

The Nikon DX format is an alternative name used by Nikon corporation for APS-C image sensor format being approximately 24x16 mm. Its dimensions are about 2⁄3 (29 mm vs 43 mm diagonal, approx.) those of the 35mm format. The format was created by Nikon for its digital SLR cameras, many of which are equipped with DX-sized sensors. DX format is very similar in size to sensors from Pentax, Sony and other camera manufacturers. All are referred to as APS-C, including the Canon cameras with a slightly smaller sensor.
Nikon has produced 23 lenses for the DX format, from macro to telephoto lenses. 35mm format lenses can also be used with DX format cameras, with additional advantages: less vignetting, less distortion and often better border sharpness. Disadvantages of 35mm lenses include generally higher weight and incompatible features such as autofocus with some lower-end DX cameras. Nikon has also produced digital SLRs that feature the larger Nikon FX format sensor that is the size of the 135 film format.
In 2013, Nikon introduced a high-end compact camera with a DX-sized sensor, the Nikon Coolpix A, featuring an 18.5 mm lens.

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1. ### I Solving the Difficult Integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##

Anyone have some ideas to approach the integral ##\int_0^{\infty} x^{n+1} e^{-x} \sin(ax) dx##?
2. ### Integrate ##\int\sqrt{4+x^2} dx##

still typing...checking latex
3. ### How to Integrate [1/(x^2 + 3)] dx?

What is ##\int \frac{1}{x^2 + 3} \ dx##? This is my attempt: ##x = \sqrt{3} \tan \theta## --> ##dx = \sqrt{3} \sec^2 \theta \ d\theta## ##x^2 + 3 = (\sqrt{3} \tan \theta)^2 + 3## ##= 3 \tan^2 \theta + 3## ##= 3 (\tan^2 \theta + 1)## ##= 3 \sec^2\theta## ##\int \frac{1}{x^2 + 3} \ dx = \int...
4. ### B Why is Delta y not equal to dy for infinitesimally dx on the graph?

Hello! As is known, \Delta y = dy for infinitesimally small dx. It's true. But if we have graph we may see that \Delta y isn't equal to dy even for infinitesimally small dx. Why is that so? Thanks!
5. ### Evaluate ##\int_{-\infty}^{\infty} e^{-|x|}\delta(x^2 +2x -3) dx##

Hi, Is it correct to say that the dirac delta function is equal to 0 except if the argument is 0? Thus, ##x^2 +2x -3## must be equal to 0. Then, we have x = 1 or -3. What does that means? ##\int_{-\infty}^{\infty} e^{-|x|}\delta(x^2 +2x -3) dx = e^{-1}## and/or ##e^{-3}## ? Thank you
6. ### MHB 1.3 find dx of (7+9x-6\sqrt{x})/x

Find $\dfrac{dy}{dx}$ for:$y=\dfrac{7+9x-6\sqrt{x}}{x}$ ok several ways to solve this but thot the best might be to expand it first so $y=\dfrac{7}{x} +9 -6\dfrac{\sqrt{x}}{x}$ or is there a better way
7. ### How can I find "dx" in a straight line of electric charge?(Picture)

This is the question ... I have it's solution ... My problem : I can't understand why dx=R/cos^2(teta) dteta I have thought many hours but I couldn't find it's reason ... Can anyone please help with this ?!
8. ### Issue converting dV to dx dy dz

I can calculate the divergence $$div A = 2y + 2x + z + 8z^3$$ Now I have to integrate over this cut-off sphere. So I decide I'll cut it up into small discs with height dy and integrate over that $$dV = \pi(4 - (y-1)^2)^2 * dy$$ My issue here is I don't know how to integrate 2x + z + 8z^3. Not...
9. ### I Probability in a small interval is ##P. dx##

Reif says " ... variable ##u## which can assume any value in the continuous range ##a_{1}<u<a_{2}##. To give a probability description of such a situation, one can focus attention on any infinitesimal range of the variable between ##u## and ##u+d u## and ask for the probability that the variable...
10. ### MHB 7.1.17 int e^{-\dfrac{x^2}{2}} dx from 0 to infty

Evaluate $\displaystyle\int_0^\infty e^{-\dfrac{x^2}{2}} dx$ ok first reponse is use IBP but can we use $e^u$ where $u=-\dfrac{x^2}{2}$ ot $u=\dfrac{x}{\sqrt{2}}$
11. ### MHB 8.2.5.evaluate int 64x sec^2(4x) dx

Evaluate $I=\displaystyle \int 64x\sec^2(4x) \, dx$ ok well first $64 \displaystyle\int x\sec^2(4x) \, dx$ off hand not sure what trig id to use or if we need to
12. ### B What's the difference between d, d/dx and dx?

What's the difference between d,d/dx and dx?
13. ### Integral of 1 / (x^2 + 2) dx ?

Mentor note: Moved from technical section, so missing the homework template. How do you integrate this? $$\int \frac{1}{x^2 + 2} dx$$ My attempt is $$\ln |x^2 + 2| + C$$
14. ### I How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?

How do you integrate ##\frac{1}{\sqrt{x^3 + x^2 + x + 1}} \, dx##? Please give me some hints and clues. Thank you
15. ### How To Integrate 1/[sqrt (x^2 + 3x + 2)] dx?

How do you integrate ##\frac{1}{\sqrt{x^2 + 3x + 2}} dx##? I had tried using ##u = x^2 + 3x + 2## and trigonometry substitution but failed. Please give me some clues and hints. Thank you mentor note: moved from a non-homework to here hence no template.
16. ### A Dx in an integral vs. differential forms

Good Morning To cut the chase, what is the dx in an integral? I understand that d/dx is an "operator" on a function; and that one should never split, say, df, from dx in df/dx That said, I have seen it in an integral, specifically for calculating work. I do understand the idea of...
17. ### Calculating Period of System with Masses, R & dX

Here is the picture on the system. I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position. In the thread...
18. E

### B Is dx Negative in Non-Standard Analysis?

This is more of a "housekeeping" question, though I haven't studied much in the way of infinitesimals so apologies in advance for my lack of rigour! As far as I'm aware, an infinitesimal can be thought of as a small change in some quantity. Changes can be either positive or negative, so...
19. E

### B The use of the dx in the quantum state vector integral

As a simple example, the probability of measuring the position between x and x + dx is |\psi(x)|^{2} dx since |\psi(x)|^{2} is the probability density. So summing |\psi(x)|^{2} dx between any two points within the boundaries yields the required probability. The integral I'm confused about is...
20. ### MHB Integrating Higher Powers of Tangent: A Shortcut Using Trigonometric Identities

7.2.6a use $\tan^2 x= \sec^2 x-1$ to evaluate $$\displaystyle I_{6a}=\int\tan^4 x \, dx$$ well my first inclinations is to. $$\int(\sec^2 x-1)^2\, dx$$ then expand $$\int (\sec^4 x - 2 \sec^2 x +1)$$ ok not sure if this is the right direction W|A returned this:
21. ### MHB 1.1.4 AP Calculus Exam Problem int sec x tan x dx

$\tiny{213(DOY)}$ $\displaystyle\int \sec x \tan x \: dx =$ (A) $\sec x + C$ (B) $\tan x + C$ (C) $\dfrac{\sec^2 x}{2}+ C$ (D) $\dfrac {tan^2 x}{2}+C$ (E) $\dfrac{\sec^2 x \tan^2 x }{2}+ C$
22. ### B Justification for cancelling dx in an integral

In Paul Nahin's book Inside Interesting Integrals, on pg. 113, he writes the following line (actually he wrote a more complicated function inside the integral where I have simply written f(x))... ## \int_0^\phi \frac {d} {dx} f(x) dx =...
23. ### Integrating (sin(x))/x dx -- The limits are a=0 and b=infinitity

U= 1/x dV= sin(x) dU = -1/x^2dx V= -cos(x). lim b--> infiniti (integral from [0,b]) = 1/x(-cos(x)) - integral(1/x^2(cos(x)) dx
24. ### B Is Understanding 'dx' Just a Heuristic in Calculus?

Hello! Let ##I## be an interval of size ##L##, suppose we divide it into bits of ##dx## then ##L=dx+dx+... =\alpha.dx## Since ##dx## is by definition infinitesimally small is it correct to imply that for each ##x## there's a corresponding ##dx## hence, here, ##\alpha## would be, theoretically...
25. ### Integration problem ∫1/(√3 sinx+ cosx) dx

Homework Statement ∫1/(√3 sinx+ cosx) dx is Ans. as per textbook 1/2(log(tan((x/2)+(pi/12)) 2. The attempt at a solution Attempt 1-I changed it to half angles (x/2) and then multiplied and divided sec^2(x/2) to the numerator and denominator, then putting tan(x/2)=t I got 2∫1/(√3t+1-t^2) I wrote...
26. ### What does 'dv and dx' mean in f = eta X A (dv/dx)?

Homework Statement What does 'dv and dx' mean in f = eta A (dv/dx) in coefficient of viscosity? 2. Homework Equations What does 'dv and dx' mean in f = eta A (dv/dx) in coefficient of viscosity? The Attempt at a Solution As I know v = velocity and x = distance. then what does 'dv' and 'dx'...
27. ### Why Do Physicists Write Integrals as ##\int dx f(x)##?

Why do physicists like to write ##\int dx f(x)## instead of ##\int f(x) dx##? And also when did that start?
28. ### I What is dx, dy and dz in spherical coordinates

What is dx, dy and dz in spherical coordinates
29. ### Extension of a rod segment dx due to a passing longitudinal wave

Let us look at short segment of a rod with its length dx. Due to longitudinal wave, left endpoint moves for s in the direction of x-axis and the right endpoint moves in the same direction for s+ds. Because I want to calculate the elastic energy of the wave motion, I need the extension of dx so...
30. ### Is it possible to find dy given the values of dx and v?

Homework Statement This isn't really a homework problem/question. I am just wondering if it is possible to calculate the vertical distance (dy) when the only given values are those of the horizontal distance (dx) and velocity (v). An example of this projectile-motion problem would be this: A...
31. ### I What are differentials and how are they used in calculus and physics?

Can dx be thought of as a sufficiently small change in x? I want to say that dx is the change in x and change in x approaches 0, but that would just be 0. So I think it might make more sense to just say sufficiently small. Then when we look at something like a derivative dy/dx we can look at...
32. ### I What is the meaning of dx and how does it relate to dy/dx?

Often I have to solve problems using dx or dq. I always don’t quite understand what’s going on. I understand what dy/dx is but not just dx. Can someone walk me through in plain language a somewhat rigorous definition of differential like dx?
33. ### I Understanding Differentials (dx, dq, etc) in Physics Problems

When solving physics problems sometimes we have to use differentials like dx or dq. I don’t quite understand how to use these. I understand that the limit as change in x approaches 0 of change in y over change in x is represented by dy/dx, where dy and dx are sometimes said to be small changes...
34. ### I Please suggest whether I should use delta or dx method.

I previously made a derivation of Neumann potential. It can be found in the pdf file below. I originally made it in the ##dx## method. It involved equations like ##dm=I dS##. My maths teacher told that such an expression has no meaning, at least in elementary calculus. However I argued that my...
35. ### A Integral ##\int_{-1}^{1} [P_{l}^{m}]^2 ln [P_{l}^{m}]^2 dx##

Hi, todos: Do you know how to calculate the definte integral for Integral for ##\int_{-1}^{1} [P_{l}^{m}]^2 \ln [P_{l}^{m}]^2 dx##, where ##P_{l}^{m} (x)## is associated Legendre functions. Thanks for your time and help.
36. ### I What Is the Integration Process for tan(2x) dx?

This is the continuation of the below thread: https://www.physicsforums.com/threads/what-is-integral-tan-2x-dx.856530/ Can someone please tell me how to integrate tan 2x dx?
37. ### I Why Denote 1 Form as dx? - Sean Carroll's Lecture Notes on GR

Hi everyone I am reading Sean Carrol's lecture notes on general relativity. link to lecture : https://arxiv.org/abs/gr-qc/9712019 In his lecture he introduced dxμ as the coordinate basis of 1 form and ∂μ as the basis of vectors. I understand why ∂μ could be the basis of the vectors but not for...
38. ### MHB How Can You Evaluate a Tricky Integral of Sin^5(3x) dx?

$\tiny{8.3.8}$ $\textit{evaluate}$ \begin{align*}\displaystyle I_{8}&=\int_{0}^{\pi/4} \sin^5{2x},dx\\ &=-\int_{0}^{\pi/4} (\sin^2(2x))^2 sin(2x) \, dx \end{align*} $\textit{set$u=\cos{2x} \therefore du=-2\sin{(2x)} \, dx$then$u(0)=1$and$\displaystyle u(\pi/4)=0$}$...
39. ### B What is the role of dx in mathematical and scientific calculations?

Hello, I am slightly confused about the actual meaning of dx. Because I read in a physics textbook, they say something along this line: "We divide this region into spherical shells of radius r, surface area 4pr 2, thickness dr, and volume dV = 4pr^2 dr." I don't understand how can we represent...
40. ### MHB Derivative of y w.r.t x: 242.7x.25

$\tiny{242.7x.25}$ $\textsf{Find the derivative of y with respect to x}$ \begin{align*}\displaystyle y&=8\ln{x}+\sqrt{1-x^2}\arccos{x} \\ &=\frac{8}{x}+? \end{align*}
41. ### I ## \int ~ dx dy dz ~ f(x,y,z)~ \delta (x+y+z-1)##

Hi all , I see this integral too much in QFT books when making loop calculations : ## \int_{0}^{1}~ dx~ dy~ dz~ \delta (x+y+z-1) = \int_{0}^{1} dz \int_{0}^{1-z} dy ## Can anyone explain how did we get this ? I mean it's apparent that ##\int_{0}^{1}~ dx \delta (x+y+z-1) ## have been...
42. ### ##\int \frac{1}{\sqrt{1-x^2}} dx##

Homework Statement I am doing a little review and having a some trouble deriving the integral ##\int \frac{1}{\sqrt{1-x^2}} dx## Homework EquationsThe Attempt at a Solution Initially I was trying to solve this integral using the substitution ##\cos \theta = x##. I drew my triangle so that...
43. ### I Integrating sqrt(x) cos(sqrt(x)) dx

Question: sqrt(x) cos(sqrt(x)) dx My try: Let dv = cos(√x) => v = 2√xsin(√x) and u = √x => du = dx/(2√x) Using integration by parts, we get ∫√x cos(√x) dx = 2√x√x sin(√x) - ∫(2√xsin(√x) dx)/(2√x) = 2x sin(√x) - ∫sin(√x) dx = 2x sin(√x) + 2 cos(√x) √x However, the answer given in the book...
44. ### How integrate 1/(x(1+x^2)^0.5) dx

Hi everyone, Can you tell me how to integrate the following equation? Integrate(1/(x(1+x^2)^0.5) dx

47. ### MHB 206.8.7.58 Int 1/(x^2-6x+34) dx complete the square

$\text{206.8.7.58}$ $\text{given and evaluation}$ $$\displaystyle I_{58}=\int \frac{dx}{{x}^{2}-6x+34} =\dfrac{\arctan\left(\frac{x-3}{5}\right)}{5} + C$$ $\text{complete the square}$ $${x}^{2}-6x+34 = \left(x-3\right)^2 + 5^2 = {u}^{2}+{a}^{2} \\ u=x-3 \\ a=5$$ $\text{standard integral}$...

50. ### MHB 205.8.4.30. Int 24/(144x^2+1)^2 dx

206.8.4.30. Int 24/(144x^2+1)^2 dx 206.8.4.30 $\displaystyle I_30=\int \frac{24}{(144x^2+1)^2}= \arctan\left(12x\right)+\dfrac{12x}{144x^2+1}+C$ So $x=12\tan\left({u}\right) \therefore du=12\sec^2 (u)du$ By the answer assume a trig subst. Didn't want to try reduction formula: Continue or is...