Dx Definition and 305 Threads

In some places in physics like proving the wave equation,we see that the physicist divides the equation by dx or \partial x or maybe cancels some of them and then says with a smile:You shouldn't tell a mathematician! I want to know the ideas of mathematicians about that and want to know why...

The reason I ask the aforementioned question is because I came across the expectation values of operators in Quantum Mechanics. And part of the computation involves integrating a function of the complex conjugate of x with respect to dx. So as an example let's say I have: ∫ sin (x*) dx where...

Not really a homework problem, but this is just a problem that's been bugging me for a while: how would you find ∫sec2x dx without "cheating" and using the simple fact that d/dx tanx = sec2x? I know it's possible using integration by parts, but I'm looking for a way using calc I level...

Homework Statement integrating x^3lnxdxHomework Equations The Attempt at a Solution i let u = lnx du/dx = 1/x xdu = dx x=e^u substituting that, i got e^(4u)udu then i let v = 4u dv/du = 4 1/4du = dv substituting that, i got 1/4integral e^v vdv I haven't gone beyond that step yet. I was...

Hi, simple question, but difficult to find an answer for me How to integrate sqrt((ax+b)/x) dx ? a,b constants and x variable if it matters, I would be happy if you could solve it just for both a,b >0 Thanks

Homework Statement I want to solve this integral without using series expansion. The answer should be in a closed form. I wonder if this is possible? Homework Equations The Attempt at a Solution I used numerical methods and was able to solve it numerically for a given...

Evaluate the integral (help)! sin2x dx b=pi/8 a=0 ∫sin2x dx b=pi/8 a=0 I'm having a little trouble finishing out the problem. This is what I've got so far. u=2x du=2dx du= 1/2dx 1/2∫sin(u) du (-1/2)cos u (-1/2) cos 2x [(-1/2)cos2(pi/8)]-[(-1/2)cos(2(0))] ? +...

Really not sure... Does anyone know an appropriate substitution? The whole problem is: Find the substitution that simplifies the differential equation x(dy/dx) + y = e^(x*y)

Say we want to find ∫(-cosx)sinx dx set u = -cosx so du/dx = sinx ∫u \frac{du}{dx}dxAnd then the dx's apparently cancel out? What is going on? I thought \frac{du}{dx} meant lim Δx→0 \frac{u(x+Δx)-u(x)}{Δx} and that the dx in the context of an integral was a representation of the Δx's from...

The problem is to solve the integral of : dx / (x^2(9-4x^2)^(1/2)) using trig substituition, which I really don't understand. Formula's that are useful: The integral table Integral 1/(u^2(a^2-u^2)^(1/2))= -((a^2-u^2)^(1/2)) / (ua^2) Work so far: Figuratively banging my head...

Interpretation of "dx" as the differential of x for Indefinite Integrals This question is concept-as-opposed-to-calculation based. I understand that when one sees the integral sign, followed by f(x)dx, that we can think of this as the indefinite integral, or antiderivative of f(x), with...

What is $\displaystyle\int\frac{dx}{dx}$? There is a reasonable answer to this question. Also, does anybody know what this integral is called?

Homework Statement ∫x*delta((x/y)-t) dx from 0 to infinity Homework Equations ∫x*delta((x/y)-t) dx from 0 to infinity = ty*|y|*θ(ty) The Attempt at a Solution Okay, so using the transformation of variables technique via the Jacobian, I see where the |y| comes from. However, using...

Homework Statement During the opening kickoff of a college football game, the kicker kicks a football with an initial velocity of 27.5m/s at an angle of 41 degrees above horizontal. What is the flight time for the ball? What is the maximum height How far does it travel before hitting the...

Homework Statement Finding ∫x sin^3x dx Homework Equations I don't think this is needed The Attempt at a Solution ∫x sin^3x dx using integration by parts u = x, du = dx, dv = sin^3x, v = 1/3cos^3x - cosx = (x)(1/3cos^3x - cosx) - ∫1/3cos^3x - ∫cosx dx = (x)(1/3cos^3x - cosx) -...

Is the derivation of this relationship ln x/y = ln x - ln y exclusively from, and originating from the evaluation of the Integral from 1 --> x 1/t dt = ln x ? To say another way can ln x/y = ln x - ln y always be considered to apply to this integral ?

Homework Statement \int x e^-3x dx Homework Equations \int f(x)g'(x) = f(x)g(x) - \int f'(x) g(x) Integration by substitution not allowed The Attempt at a Solution f(x) = x, f'(x) = 1, g'(x) = e^{-3x}, g(x) = \int e^{-3x} dx = -\frac{1}{3}e^{-3x} \int x e^{-3x} dx =...

To get something into integral form the dx needs to be at the end right? How can I do this if what I have is rsin(x+dx)cos(x+dx)?

Homework Equations dL = L0αdT ΔL = L0αΔT These two equations are both listed separately on my equation sheet. How are the dL and ΔL terms different?

Homework Statement Hi, I'm trying to solve this problem and guess I'm doing something wrong. Evaluate Integral tan(x)^5*sec(x)^4 dx Homework Equations integral tan(x) dx = ln(|sec(x)|) integral tan(x)^n dx = tan(x)^(n-1)/(n-1) - integral tan(x)^(n-1) dx tan(x)^2+1=sec(x)^2 The Attempt at...

Homework Statement Evaluate integral sqrt(x^2-9)/x dx Homework Equations The Attempt at a Solution I get this for my answer sqrt(x^2-9)+3sin^(-1)(3/x)+c which is apparently wrong because when I take the derivative of it I don't get the integrand my work is a attachment in this post wolfram...

Homework Statement Evalute the integral ∫ [x / 1 + x] dx Homework Equations ∫ [x / 1 + x] dx The Attempt at a Solution I forgot how to do solve this type of integral, or never had enough practice. And this problem is actually for a physics problem :-) And my algebra is very...

Is it any good? I mean scientific papers on arxiv. I'm contemplating buying some kind of tablet vs kindle dx for this purpose.

My question is based around when you integrate dx as if it were a function and when it just represents the quantity that is infinitely small. Say we have the function y=3, a straight horizontal line. We want to find the area under this line from x = 0 to x = 10. I know, you wouldn't use...

I saw someone post some issues they had with their car and got some good help, so I figured I would try here. I have a 1995 honda civic dx, automatic, ~170k miles. I had the transmission fluid flushed maybe 3k-4k miles ago. When I first start driving the car, generally if the car has been...

"f(x) dx = f" Two related questions, or bundles of questions. First, I read in Spivak, Calculus, p. 244, Ch. 13: (Here f:\mathbb{R} \rightarrow \mathbb{R}.) Any comments welcome! It seems like a useful thing to have a symbol for, and it would be handy to have one that could be used in...

Homework Statement i)Use integration by parts to express: I(n) = ∫ sin^n (x) dx in terms of I(n-2). ii) Hence show that ∫(π/2 for top, π/4 for bottom) 1/[sin^4 (x)] dx = 4/3 Homework Equations Reduction Formula and Trig Identity [sin²(x) + cos²(x) = 1] π = pi The Attempt at a...

so I just introduced myself to the concept of integration by parts a few days ago, and today for practice I decided to try to redo one of the examples given in a youtube video without the assistance of youtube. That problem was int. (x^2)(e^x) dx, for which the answer is (e^x)(x^2 -2x + 2). So...

If y = f(x) , and ( dy / dx ) + ( y / ( sqrt(a+(x^2)) ) ) = 0 I knew its solution is y = { sqrt(a+(x^2)) - x } , where a is a constant can anyone give the proof , by solving the differntial equation. Are there any other solutions for the above given differential equation. I asked this...

Hi, Part of solving a differential equation involves integrating M(x,y) with respect to x, where M(x,y) = x + tan-1(y). What are the steps to integrating the arctan portion? \int tan-1(y) dx Thank you.

Homework Statement ∫〖Sin^(2 ) x * cos2x dx〗 Homework Equations The right answer should be: sin 2x / 4 - x/4 - sin4x / 16 The Attempt at a Solution If i would set Sin^(2 ) x= (1-cos2x)/2 I can replace it in the integral Then we get: ∫▒〖(1-cos2x)/2 cos2x dx〗 As far as I am...

Homework Statement $1/cosx dx Homework Equations See the scanned paper The Attempt at a Solution See my scanned paper [PLAIN]http://img812.imageshack.us/img812/2892/img0003001.jpg

i have two problem 1- (-3x+2y)dy=(x-2y)dx 2- y*dy= - (y+cos x ) dx pleeeeeeeeeeeeeeeeeeeeeezzzzzzzzzz help me quiqly:frown:

Homework Statement I need help with an integral, since my calculus skills aren't the greatest. I need help with getting from this \pik\sigmay\int \frac{2x dx}{(x^{2} + y ^{2})^{3/2}} (i) to this \pik\sigmay\frac{-2}{(x^{2} + y ^{2})^{1/2}} (ii) I integrate from 0 to a (didn't...

Homework Statement Well gentlemen, another year, another integral eh? Anyways, \int \frac{1}{x^4+4}\,dx I really want to do this without looking at Wolfram/Google. Homework Equations U-substitutions, parts, partial fractions The Attempt at a Solution Basically I tried to...

Homework Statement x = (1/2)(u^2 - v^2), y = uv find \delta{x} and \delta{y} Homework Equations - The Attempt at a Solution I think its simple enough but I don't know what sort of method to use to answer this. Any help would be really awesome :)

I'm not understanding why my answer is wrong Homework Statement \inttan^3(x) dx This is the solution I've been getting for this problem, but I notice you get a different answer when you let u = tan(x) and du = sec^2(x) dx Homework Equations tan^2(x) = (sec^2(x) - 1) The Attempt at a Solution...

Homework Statement Can I solve for xlnx = c + dx using Lambert's W function? Homework Equations The Attempt at a Solution

I'm self-learning calculus. I'm not good at maths. Well, I just tried to solve a random problem in a math software Integral [ Sin^(-1) x ] dx The solution is here: http://img43.imageshack.us/img43/4597/60496310.png Now the problem is I don't how it's going. How do we get to step 2...

Homework Statement derive a reduction formula for ∫(lnx)n dx and use it to evaluate ∫1e (lnx)3dx Homework Equations The Attempt at a Solution In other examples we've started by saying ∫(lnx)ndx = ∫(lnx)(lnx)n-1dx and using integration by parts. So let: f = (lnx)n-1 f' =...

I just started taking physics this year (junior year in high school) and I can honestly say that I have no idea what's going on. Alright, so I know about free fall (well...the falling part of free fall, not when the ball bounces up and back down again) and acceleration, but pretty much anything...

Hi everyone, once I again I turn to all of your expertise in complex analysis. Homework Statement Evaluate \int\frac{(ln(x))^{2}}{1+x^{2}}dx from 0 to +infinity by appropriate series expansion of the integrand to obtain 4\sum(-1)^{n}(2n+1)^{-3} where the sum goes from n=0 to...

Homework Statement Integrate Homework Equations integrating following equation about dx: (b1-(b1*x/L)+(b2*x/L))^2 The Attempt at a Solution I expanded all terms than integrated. I used integration by part to get it down to this but I am curious to see if there's better way to...

Dear I am trying to integrate the following equation f=exp(m*x) dx where x =[x1 , x2] is a vector of variable could you help me please to find the solution when I would like to integrate like this kind of equations. help appreciated Best Regards

Hi I have an integral as follows, int((1/x)exp(-x),x,0,s) I want to integrate from [0,s). My question is how to integrate without including s as the upper bound. Any help will be appreciated

Homework Statement I haven't done much math for years. just a little reminder would be very appreciated. when you take integral for (2x^2+1)/x dx I believe this can break down into integral 2x dx + integral 1/x dx What I wondered about was is this summation of those two as...

A quote from the book of T.L. Chow 'Mathematical methods for physicists' The reader may notice that dy/dx has been treated as if it were a ratio of dy and dx, that can be manipulated independently. Mathematicians may be unhappy about this treatment. But, if necessary, we can justify it by...

I try to solve the integral 1/(1+x^3) dx , but I got stuck Now I got as solution: (1/3) ln(x+1) - (1/6) ln(x^2 -x+1) + (1/2) integral (1/(x^2 -x+1)) Can someone help me to solve the last integral? I have absolutely no idea how I can solve that one.. So integral: 1/(x^2 -x+1) dx

Integral 1/(1-x^2y^2) dx? From 0 to 1 Where x = sina/cosb and y=sinb/cosa Using substitution and changing the limits yields Integral from 0 to pi/4 of cos^3(a)cos(b) / (cos(a+b)cos(a-b)) du But how to go from here?

Homework Statement Can someone help me integrate (4x - 3) / (x^2 +1) ? The Attempt at a Solution I'm doing my maths baccalaureate in 2 days and came across this question today! I don't know where to start i.e. which method to use: Integration by parts definitely does not work...