Dx Definition and 305 Threads

there was this curve where Dy/Dx = 3-x/y+4 so he cross multiplied the equation as (3-x)Dx=(y+4)Dy , then he proceeded to integrate the function . i don't know if this is correct or not , i mean Dy/dx is just a notation , how can you treat as if it was just a normal fraction ? i thought...

I'm doing integration by parts and I am a bit confused as to what exactly dx is. Usually when integrating it is just dropped or forgotten about. Now when doing integration by parts there are some problems where you pick x as your u and dx as your du. since du is the derivative of u why isn't the...

dx as change in distance vs dx as infinitesimal x? Why are they the same notation?Sent from my iPhone using Physics Forums

Homework Statement ∫e^x lnx dx I don't really know how to solve it. The Attempt at a Solution This is what i have: ∫e^x lnxdx = lnx e^x - ∫e^x/x dx And my prof says its wrong, that i can go further with it with some method they discussed about ( i missed it :(

Homework Statement ∫(4x)/(x2+9) dx Homework Equations The Attempt at a Solution Originally I tried to solve with u substitution: u=x2+9 du=2x dx 1/2du=dx ∫2/u =2lnu+C =2ln(x2+9)+C But shouldn't arctan be somewhere in the answer?

Homework Statement integral of Sech^5(x)*Csch(x) dx Homework Equations I think Coth^2(x)-1 = Csch^2(x) may help The Attempt at a Solution I tried a few things. The latest being breaking the problem up and doing some re-working. int(Sech^2(x)*Sech^3(x)*Csch(x) dx) I then...

Homework Statement Solve the differential equation: dy/dx = y+3 Homework Equations The Attempt at a Solution When I try to integrate with respect to x, I get ∫dy/dxdx - ∫ydx=∫3dx→y-∫ydx=3x So what does one do about the integral of y with respect to x? There is nothing...

this is an euler lagrange equation problem from the book- "classical mechanics-John R. Taylor", problem-6.11 find the path function for which ∫ √x*√(1+y'^2) dx is stationary. the answer is- x= C+(y-D)^2/4C, the equation of a parabola. here the euler lagrange equation will work on...

Homework Statement I have to find the power series representation for integral (1/x) dx Homework Equations ln (1+x) The Attempt at a Solution This is very similar to ln(1+x) but I don't know if this helps me. Is this ln(x) shifted one to the right? So maybe I can use what is...

What is the integral of 1/(x^3 + bx - c) with respect to x? This is part of a larger problem I am working on, but finding the integral has proved a sticking point. I have simplified it as much as possible. P.S. The larger problem is finding J(r) in this PF post...

[HELP] How to integrate ∫ 1/(1-cosx)^2 dx ?? Hi all, A very fundamental question here, but I cannot find solution from calculus books. Anyone know how to integrate ∫ 1/(1-cosx)^2 dx ?? Thanks.

∫x(dx)^2=? and what is the difference between dx^2 and (dx)^2?

Homework Statement Consider the integral INT -2x/(1+x^2) dx FROM -INF TO INF (The attached TheIntegral.jpg file shows this in a more aesthetically-pleasing manner.) If the integral is divergent, state that it is so. Otherwise, evaluate the integral. Homework Equations Integration...

Ok, so we know that x=rcos(\theta) So what is dx? *** Furthermore, can I get dS in polar by finding dx and dy in polar and then substituting them into dS for rectangular? Is there an easier way to solve for dS in polar?

Homework Statement Integral of sin(x) sin(x+1) dx from 0 to 2pi. Homework Equations Integration by parts: Integral u dv = uv – Integral v du The Attempt at a Solution My work has been attached as MyWork.jpg. I, basically, get 0 * integral_I_started_with = something_else instead of...

Homework Statement Integral x^3sqrt(4x^2 -x^4) dx Homework Equations Maybe something from a table The Attempt at a Solution I pulled the x^2 our from under the square root. ∫ x^4 (sqrt(4-x^2)) dx I'm not sure how I can do this one. Maybe it can fit the forum ∫ usinu du ?

Homework Statement Integral of 5x^2 /sqrt(4x-x^2) dx. (This can also be seen in the attached TheProblem.png file.) Homework Equations Integration with variable substitution. The Attempt at a Solution Could someone please tell me what I did wrong in my work (which is attached as...

Homework Statement This ( http://www.wolframalpha.com/input/?i=integrate+cos%5E6+(x)+dx+from+0+to+pi%2F2 ) is the integral I am trying to evaluate.: int cos^6 (x) dx from 0 to pi/2 Homework Equations (1 + cos(2x))/2 = cos^2 (x) (1 – cos(2x))/2 = sin^2 (x) sin^2 (x) + cos^2 (x) = 1...

I'm having a hard time breaking this down using tri identities. } = integral sign 20}sec^3(x) dx 20}sec^2(x) * sec(x) dx 20}[tan^2(x)-1] * sec(x) dx after this I'm stuck. I tried letting u = tan(x) or sec(x) but i can't seem to cancel anything out.

Show that ∫ logb(x) dx = x ∙ ( logb(x) - 1 / ln(b) ) + C can you show me the complete solution to this prob? thanks!

Homework Statement The integral of 5/(x^2 + 1) dx from -1 to 1. (The TheIntegral.jpg attachment shows this in a aesthetically-pleasing way.) Homework Equations sin^2 (θ) + cos^2 (θ) = 1 1 + tan^2 (θ) = sec^2 (θ) cot^2 (θ) + 1 = csc^2 (θ) x = tan(θ) x = cot(θ) The Attempt at a...

So dx means an infinitesimally small change in x. Why is the slope written \frac{dy}{dx} instead of \frac{f(x)}{dx} since you are only making the x component infinitely small? When you take the integral you do ∫f(x)dx not ∫dy*dx

Homework Statement What is the compensation factor for converting dy dx to cylindrical coordinates? Homework Equations None that I know of besides the bottom ones as part of the attempt The Attempt at a Solution So I know that the conversion formulas for going from Cartesian (x,y,z)...

How to find the integral of sin x dx? $$\int sin x dx=?$$

Homework Statement Integrate ∫dx/(sin(x)+a), where a is a constant.Homework Equations The Attempt at a Solution I have been working on this for a while, and for some reason I can't figure it out. The attempt that seemed the most promising to me was to multiply top and bottom by (sin(x)-a)...

evaluate : $\int_{0}^{2\pi}x^2 cos(nx)\, dx$

I understand from the equation: df = {\frac{\partial f}{\partial x}} dx + {\frac{\partial f}{\partial y}} dy that: dx \neq \partial x . I understand why df \neq \partial f (df is the change in f when the change in all the variables is infinitesimal, and \partial f is the change in...

Hello, I was just wondering why the integral of force over dx becomes kinetic energy

Hi guys I have a doubt. How can I prove that (∫ (from 0 to pi) sin^7 xdx)(∫ (from 0 to pi) sin^(7/6) xdx)^6 is at most 128 But how can I prove that the lower bound of this expression is (pi/2)^7I think is a very interesting and not an easy question so any ideas? A guidance or something...

Hi, Homework Statement I have already evaluated the integral 1/sqrt(x)exp(-ix) using The Residue Theorem and now I was looking for another method. So I thought of applying integration by parts and I got this attached formula. Now I am wondering how to evaluate this series. My first...

Proposition. $\displaystyle \int\frac{dx}{x^2}=-\dfrac{1}{x} $ Proof. $$\begin{aligned}\int\frac{dx}{x^2}&=\int\dfrac{dx}{x\cdot x} \\&=\int\dfrac{d\;\not x}{x\cdot \not x}\\&=\left(\int d\right)\frac{1}{x}\\&=id\left(\frac{1}{x}\right) \\&=\frac{1}{x}\end{aligned}$$ Now, using the well-known...

Hi, I am just doing this out of curiousity. Homework Statement I want to integrate 1/sqrt(x)exp(ix) dx from minus infinity to infinity. Homework Equations The Attempt at a Solution I had a couple of ideas one was to substitute x=u^2 but then you mess up the limits and...

∫1/(1+x^4) dx, from 0 to ∞ I have tried integration per partes, several different substitutions and transformation into different coordinate system but i have always only found another equivalent integral that i was not able to solve... I have also performed a numerical integration, but...

Hi all can please explaine to me what is integration of y/(x^2-y^2) dx step by step ...

Hi all what is integration of 1/(x^2-y^2) dx

Good day! I was trying to make sense of the notation $P(X \in dx),$ where $X$ is a continuous random variable. Some also write this one as $P(X \in [x, x+dx])$ to represent the probability that the random variable $X$ takes on values in the interval $[x, x+dx].$ I have seen similar notation a...

Here is the question: Here is a link to the question: How do you evaluate this integral: ∫ 4 (tan^3)x dx? - Yahoo! AnswersI have posted a link there to this topic so the OP can find my response.

Homework Statement Integrate (3x^2-10)/(x^2-4x+4) dx using partial fractions. Homework Equations None The Attempt at a Solution I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2. I've also tried using (Ax+B)/(x-2) + C/(x-2)^2 Though I...

I've been reading in my engineering textbooks and came across a frequent equation manipulation that involves multiplying/bringing the dx term of dy/dx to the other side of the equation, and then integrate both sides. I don't know what technique this is and I can't find it in my Stewart's...

I have a question to ask, is dx = δx, can they cancel each other like \frac{dx}{δx}=1 and is it mean that: \frac{δf}{δx}\frac{dx}{dt}=\frac{df}{dt}? (f = f (x,y,z))

hi, Reading a book on thermodynamics and the guy often uses something like this : ∫1/T dQ = ΔS and then he says "this in differential form" : dQ/T = dS I kind of get the idea visually that one slice of "integral" will be dQ and you can think of it this way. But my question is how...

Homework Statement ∫x^3*√(x^2-5) dx Homework Equations ∫u.dv=u.v-∫du.v The Attempt at a Solution So i tried to change the integral to ∫x*x^2*√(x^2-5)dx and u = x^2-5, then du = 2x, so 1/2*∫x^2*√(x^2-5) . Let u = √(x^2-5) , du = x/√(x^2-5) and dv = x^2 , v = x^3/3. Am I going in...

∫Homework Statement "Express the integrand (what does "integrand" mean?) as a sum of partial fractions and evaluate the integrals. ∫(x + 4)/ (x^2+5x-6) dx Homework Equations The Attempt at a Solution x^2+5x-6 = (x-1)(x+6) Gives: ∫ A/(x-1) + B/(x+6) dx Findig A and B: A(x+6) + B(x-1)...

Hi all. I am having Calculus 1 this year. We are using a book called Thomas Calculus. I think its a lot of fun, but I have to work very much since there is basic stuff like trigonometry that I know really bad. Since I work so much with math I thought it could be fun and helpful to talk with...

I'm curious about the general solution to \int_{-\infty}^{+\infty} \exp[P(x)] dx Where P(x) is a polynomial in x with real coefficients and whose leading (highest) order is even and its leading order coefficient is negative. Intuitively these integrals ought to converge, but I'm having...

Spring Compression problem!- PLEASE SOMEONE HELP! PLEASE! DX<? Spring Compression problem! A 2.4kg block is dropped onto a free-standing spring with k=1100N/m from a height of 1.7m above the spring. What is the spring's maximum compression? Okay, so I drew a picture of the situation. Frame...

Homework Statement Solve the equation \sin(2x) dx + cos(3y) dy = 0, where y(\pi/2) = \pi/3 Homework Equations N/A The Attempt at a Solution I understand the process that gets from the original equation to y = \frac{\arcsin(\frac{3}{2} (\cos(2x) + 1))}{3} However, I don't understand why...

∫(cot^4 x) (csc^4 x) dx Wolfram wants to use the reduction formula, but I'm meant to do this just using identities and u substitution. I was thinking something along the lines of: =∫cot^4 x (cot^2 x + 1)^2 dx =∫cot^8 x + 2cot^6 x + cot^4 x dx but I don't know where to go from there.

Function is (x - 2xy + e^y) dx + (y - x^2 + xe^y) dy = 0 Okay so it is the standard convenient exact equation for newbies. Now here is the part that confuses me. (a) Let P(x,y) = (x - 2xy + e^y) dx & Q(x,y) = (y - x^2 + xe^y) dy The function is defined for all real Numbers on an x,y plane...

During maths class last semester this integral came up in the course of discussion and my lecturer gave a quick outline of how to solve it but I didn't grasp it at the time and we moved on. I'd like to know how to do it though! The integral is: \int sin^{2}(x) The next step was: \int...