Dx Definition and 306 Threads

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. F

    Find the integral of xcos5x dx

    Homework Statement Find the integral of xcos5x dx Homework Equations uv- (integral)vdu The Attempt at a Solution I tried to pick u=cos5x and dv=xdx, but the book uses u=x, dv=cos5x dx Why can't my way work?
  2. G

    Solving Integral of "(u)^2 dx": Steps to Turn dx into du

    To find: Integral of "cos(x)^2 dx" This becomes: Integral of "(u)^2 dx" Where: u = cos(x), du/dx = -sin(x) Problem is, du = -sin(x)dx... where do I get the -sin(x) from? If it was 16dx, I could multiply everything by 16/16, move 16/1 inside the integral, couple it with dx, and switch...
  3. J

    Integrating 1/(1+sqrt(2x)) using u-substitution

    Homework Statement Find the indefinite integral. ∫ (1/(1+sqrt(2x))) dx Homework Equations ∫ 1/u du = ln |u| + CThe Attempt at a Solution I tried a couple 'u' substitutions, which didn't work out. I also tried rationalizing the denominator, but that didn't help. No one I've talked to knows how...
  4. R

    Calculating the Antiderivative of (-4x)/(x^2 + 3) dx

    Homework Statement the antiderivative of (-4x)/(x^2 + 3) dx Homework Equations The Attempt at a Solution i got -2+c is that right at all, if not can somebody help me
  5. P

    How Can dx and dy Be Manipulated in Differential Equations and Integrals?

    1. Why can dx and dy be moved around in DE (a bit but not exactly like fractions)? 2. What is the justification that allows one to operate with dx and dy after the integral signs as if they were differentials?
  6. M

    For which value of a does int e^(ax) cos(x) dx converge?

    Homework Statement For which value the definite integral (0 to infinity) e^ax cos(x) dx converges? Calculate for the value of a. Mathieu
  7. B

    Integrate secx(tanx - secx) dx

    Homework Statement Integrate... secx(tanx - secx) dx The Attempt at a Solution secxtanx - sec^2x dx = secx - tanx + C is that right?
  8. N

    Integrating (1/(1+e^x)) dx: Challenges and Solutions

    I need to find the integral of (1/(1+e^x)) dx. ...I don't think I can use u substitution, but well, I'm basically open to suggestions.
  9. B

    What is the Significance of dx in Integrals?

    What is dx mean in intagral?
  10. S

    How Do You Integrate sqrt(1 + sec^4(x))?

    Homework Statement solve : ∫ sqrt (1+sec^4(x)) dx Homework Equations The Attempt at a Solution I tried to do the substitution rule but it makes the problem more complicated
  11. L

    Integral cos(ax) / [(x^2+b^2)^2 dx

    Homework Statement \int^{\infty}_{0} \frac{cosax}{(x^2+b^2)^2} dx (a > 0, b>0) the answer (from the text) is \frac{\pi}{4b^3}(1+ab)e^{-ab} Homework Equations I have just completed the proof for a similar question in the text (easier) which was \frac{cos(ax)}{(x^2+1)} dx...
  12. S

    What is the proof for du = f'(x) dx in substitution method for integrals?

    Hello, While solving integrals using substitution method, we often come across this, if u = f(x), du = f'(x) dx I would like to know if there exists a proof for the above equation. The problem is, I am totally dissatisfied by the explanation provided to me in the classes. During the...
  13. A

    How to Solve the Integral of x arctan x dx?

    Homework Statement \int x \arctan x \, dx The Attempt at a Solution By parts, u = \arctan x dv = x dx du = \frac{dx}{x^2+1} v = \frac{x^2}{2} \int x \arctan x \, dx = \frac{x^2}{2}\arctan x - \frac{1}{2} \int \frac{x^2}{x^2+1} \, dx Again...by parts u = x^2 dv...
  14. L

    Integral of G(x,y): dx vs. dy vs. ds

    If you have a curve integral, what is the conceptual or physical difference between integrating G(x,y)dx, G(x,y)dy and G(x,y)ds ?? How do you know when to do either one?? Confused. :shy:
  15. L

    Integrating Perfect Cube in Denominator: 2/(x-2)^3 dx | Homework Solution

    Homework Statement \ 2/(x-2)^3 dx Basically integrating a perfect cube in the denominator with a constant in the numerator Homework Equations The Attempt at a Solution i thought it would be a form of ln(x), but then, that would mean having atleast some x terms in the numerator...
  16. C

    How to integrate int -1/(x^2 +1)^2 dx

    Homework Statement Find the following intergral... Homework Equations \int{\frac{-1}{(x^2+1)^2}dx} The Attempt at a Solution I can't get anywhere with this... any hints?
  17. 4

    What is the Integral of 3x (sinx/cos^4x) dx?

    can anybody help me with this problem Evaluate : integral 3x (sinx/cos^4x) dx
  18. S

    Need Help Solving Physics Problem with T, Dx, and Angle

    I have a problem. Given: T=1.05s Dx=46.1feet Angle=15 Degrees. I need to find Vx and Vy and Vi and Dymax. Can anyone help me set up the problem? for each thing I need to find...:frown:
  19. B

    Calculate int_0^infinity x^3/(e^x -1) dx

    Hi, can someone help me out with this question. Using f(t) = t^2 = \frac{{\pi ^2 }}{3} + 4\sum\limits_{n = 1}^\infty {\frac{{\left( { - 1} \right)^n }}{{n^2 }}} \cos \left( {nt} \right), - \pi < t < \pi and Parseval's Theorem deduce the identity \sum\limits_{n = 1}^\infty {\frac{1}{{n^4...
  20. Gokul43201

    Murphy's Visit: Investigating Sounds from My Honda Accord DX

    Murphy finally got to my car! I own a 1992 Honda Accord DX (160K mi on it) that's been running fine until a couple days ago. 1. Now, when I start the car, for about the first half a second or less - as the engine comes to life - there's a rattling sound that I hear from the rear of the car...
  21. B

    ODE problem: 3x^2 y dx + (x^3 + 2y)dy = 0

    I have two ODE with which I cannot to slove; 3x2ydx+(x3+2y)dy=0 I tried to change of variable y=v*x, but I still cannot find a way to solve it. the second is: (exsin(y)-2ysin(x))dx+(excos(y)+2cos(x))dx=0 here I have no idea thank you B
  22. C

    When Can Physicists Treat Symbols Like Ordinary Variables in Equations?

    Physicists do it all the time: playing around with those symbols like \frac{dx}{dt}. They just treat them like ordinary variables, which they certainly are not. Let me give you an example: If you want to change an integration variable from, say, x to r and you know that r^{2}=a^{2}+R^{2}-2Rx...
  23. J

    Integral of (sin (x))^1/2)(cos^3(x)) dx

    Not really sure where to begin on this integral. Hope this reads alright on here. Integral of (sin (x))^1/2)(cos^3(x)) dx
  24. N

    Integrate this indefinite integral: 1/(x-6)^2 dx

    I need to integrate this indefinite integral: 1/(x-6)^2 dx Here is my work... Let u= x-6 du/dx=1 so: integral 1/u^2 du = 3/u^3 + c (constant) =3/(x-6)^3 + c Have I gone wrong? And if so where? Thanks
  25. C

    Evaluating $\int_{-\infty}^{\infty} \frac{A^2}{(x^2+a^2)^2} dx$ - Chen

    Anyone has any idea how I could go about evaluating this one? \int_{-\infty}^{\infty} \frac{A^2}{(x^2+a^2)^2} dx (I have the final answer, I need a method of solution though.) Thanks, Chen
  26. T

    How Do You Integrate 2x sin(x^2) dx?

    may i know how to integ [2x sin (x^2) dx]??the answer is -cos(x^2) thanx...
  27. A

    The Natural Logarithm and the Mysterious Constant e

    why does d e^x / dx = e^x ?
  28. T

    Finding integral sin(x) cos(x) dx

    I'm having trouble with the following integral: \int {\sin x \cdot \cos x{\rm{ dx}}} I've tried to use integration by parts but that doesn't seem to get me anywhere...any tips?
  29. T

    Approximate the integral int (1 - cos x)/x dx using Taylor expansion

    I am supposed to find an approximation of this integral evaluated between the limits 0 and 1 using a taylor expansion for cos x: \int \frac{1 - cos x}{x}dx and given cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!}... i should get a simple series similar to this for...
  30. J

    How can I solve this integral using integration by parts?

    Hi , I am having trouble integrating this problem. Integrate x^2 sin(x^2) dx Here is what i did. I used the substitution method. u = x^2 sqrt u = x du = 2x dx du/2x = dx du/2 sqrt u = dx since sqrt u = x substituting this in the equation u sin(u)...
  31. G

    How to integrate int (x^2 + 4)^(-1/2) dx Is it a substitution?

    I need help antidiffing this equation: (x^2+4)^(-1/2) i have tried subbing u=x^2+4 i have tried subbing u= (x^2+4)^(-1/2). i have tried making x the subject. even tried to use partial fraction, with no avail, because i could not figure out how to use partially factorize it. If anyone could...
  32. G

    When does Ax2 + Cy^2 + Dx + Ey + F = 0 represent a parabola

    1. Determine the restrictions on the constants A, C and D so that Ax^2+Cy^2+Dx+Ey+F=0 represents a parabola that opens to the left. I know that A=0, how do u know if CD>0 or CD<0...?? 2. The equation Ax^2+By^2+Cy=0 represents an ellipse. If 0<A<B<C, then the vertices of the ellipse are on a...
  33. B

    What is the Integral of dx/ (1+cos ^2(x)) Using Different Approaches?

    for the life of me i can't seem to understand how to the the intergral of dx/ (1+cos ^2(x))?
  34. N

    Solve : 9 cosh9y dy = 4 sinh 4x dx

    I did this: 9 Integral cosh9ydy = 4 Integral sinh4xdx 9/9 sinh9y + C = -cosh4x C = - cosh4x -sinh9y Is this right , or wrong, or is there more to it.
  35. N

    Can This Differential Equation Solution Be Simplified Further?

    I did the following: dy/(y^2 -4 ) = dx Integral ( -1/4 /y + 2 + 1/4 / ( y-2) . dy = Integral dx -1/4 ln | y + 2 | + 1 /4 ln |y -2 | + C = x Multiplying all thru by - 4 we get ln | y + 2 | + ln | y - 2 | + 4C = 4x ( Note: 4C is another 'C'which is a bigger C) ln | y + 2 / y -...
  36. E

    Integral from 0 to pi/2 of (x*[sin x]^2) dx

    Hello everyone, I was solving an integral, but I am not quite sure for the final answer. If someone has the time, just take a look. Integral from 0 to pi/2 of (x*[sin x]^2)dx I used by parts integration; using u=(sinx)^2 du=2 sinx cosx...
  37. O

    What is the Integral of the Square Root of x^3 - 1?

    integral of sqrt(x^3 -1) dx. I have tries it with trigonometri subs, but I only found till integral of 2/3(sin^5/3 (tetha) / cos^2 (tetha) ) d(tetha)
  38. E

    Difference between a differential, dx, and the change in a variable, delta x?

    What's the difference between a differential, dx, and the change in a variable, delta x? Is dx the change in a variable with respect to a function while delta x is the change in the domain?
  39. B

    How to Solve Integrals with a Linear Denominator?

    quite simple but need some help: ∫ x/(4-x) dx. when there's ∫f'(x)/f(x) you can use natural log but waht about this full workings or some tips anyone? Thanks.
  40. U

    If int_a^b f(x) dx = a+2b, then what is int_a^b (f(x) + 5) dx equal to

    If \int_{a}^{b} f(x)dx = a+2b then \int_{a}^{b} (f(x)+5)dx = ? Here's what I did: \int_{a}^{b} (f(x)+5)dx = \int_{a}^{b}f(x)dx+\int_{a}^{b} 5 dx \int_{a}^{b}f(x)dx+\int_{a}^{b} 5 dx = a+2b + 5b - 5a \int_{a}^{b} (f(x)+5)dx = 7b-4a Did I do this correctly? I know the answer is correct...
  41. Q

    Understanding the Differences Between Indefinite and Definite Integrals with DX

    :bugeye: Well, I love calculus. But sometimes, its confusing. Ever been though a time while you haven't been to a single calc class, and just learn it all though reading a textbook not being able to ask questions? It's hard. I'm having a problem. f (x) = (integral sign) F(x) dx...
  42. C

    Calculus Problem Help Integral of (secx)^3 dx

    Hi all, I am stuck on this trig integral problem. The answer is provided in the book, but I do not know how to get it. The problem is this: Integral of (secX)^3 dx it says first use integration by parts: u = sec x du = sec x tan x dx dv = (secx)^2 dx v = tan x...
  43. W

    Find dx in a Complex Integration Problem: Anti-Derivative of Cos(2x)

    how would i find the anti-derv. of (cos(2x)). I am really confused with sub. ok i'll use u-du u = 2x du = 2 dx dx = 1/2 du k so... cos(u)*dx since the dx is there, you plug in the dx that i found right? so... sin(2x)1/2 ok so that's a simple integration problem, can someone...
  44. W

    Why Dropping the Sqrt{1 + 1/x^4} dx Matters for Surface Area

    ok I know how to solve for the volume no prob, but when you find the surface area, in all the proof they always drop the root, because something about being bigger than one Sqrt{1 + 1/x^4} dx can someone explain why they drop that, and how it's possible to have finite volume and infinite...
  45. F

    How to Integrate 1/(1+2x+x^2) dx Without Getting Stumped

    In an exam i stumbled when i saw this q integrate: 1/(1+2x+x^2) dx help
  46. N

    Integrate exp(-x^2), dx

    hi all, i've tried to solve this thing with Derive, but it gave me some vague erf(x) function (error function??). Is there some gosu-mathematician who can help me solve the integral? \int exp(-x^2) dx tnx
  47. V

    Calculating the Integral of (cos x)^2: Possible or Impossible?

    Do anyone have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like cosxcosx+sinxsinx=1, but it didn't help. Thank you!
  48. A

    Techniques for Integrating the Cotangent Function

    well, can somebody please tell me how do i get that: Integral of cot(x)^2 dx == -x - cot(x) what technique of integration should be used here?
  49. M

    Fun problem: ? x / (x^2 + 6x + 10) dx

    Fun problem: ? x / (x^2 + 6x + 10) dx Integration by parts proves 1=1! My mathematical fame is at hand! So how would you do this one?
  50. P

    What is Lonewolf's proposed method for integrating Ln[x]dx?

    Integrat Ln[x]dx!
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