Integration Definition and 1000 Threads

Homework Statement I was revising the topic on the evaluation of fugacity of liquids and gases for my chemical engineering course, when I ran into an equation which I think, may be wrong as I think it may evaluate to ln0, which is infinity. Here is a snapshot of the equation: The equation...

Homework Statement Evaluate the limit 1 1 1 lim ∫ ∫ ... ∫ cos^2((pi/2n)(x1 + x2 +... xn))dx1 dx2 ... dxn 0 0 0 n→∞Homework Equations Well, I know that we can change this using a double angle rule, so that the integrals become 1/2 + 1/2 cos (2*pi/2n)(x1 +...

Homework Statement Evaluate: I(y)= \int^{\frac{\pi}{2}}_{0} \frac{1}{y+cos(x)} \ dx if y > 1 Homework EquationsThe Attempt at a Solution I've never seen an integral like this before. I can see it has the form: \int^{a}_{b} f(x,y) dx I clearly can't treat it as one half of an exact...

Hello. I am in an undergraduate math major in an introductory graduate class on integration theory and it has truly been an unpleasant experience. I feel the instructor(who is teaching it for the first time) is pretty much completely disconnected from the students in his assignments and...

Homework Statement [/B] Use integration by substitution to evaluate the integral, I = \int^{x}_{x_{0}} (3 + 4t)^{\frac{5}{3}} dt Homework EquationsThe Attempt at a Solution I am confused by this question, and think that the limits on the integral might be a typo. Does it make sense for them...

As a physics major, I felt devastated today when I had to face the toughest integrals in my life for advanced quantum mech course. I am really embarrassed I did bot learn integration properly. please suggest me a good book that will help me excel in sort of integraion I will face for QM and...

Hi, I'm trying to understand why When you write a*dt = dv then you can write the integral like this., ∫dv (from v0 to vt) = ∫a*dt (from 0 to t) My challenge is this: from the equation a*dt = dv, the term "dv" geometrically means an infenitesimalle small change in function value of the...

Hello, My question is, there is a concept of contour integration. Which is choosing a circular contour space sort of, and integrating along that. How do you do contour integration? Secondly, there is something going around called integrating along a square. I tried searching only, a lot...

Suppose $\int f d\mu < \infty.$ Let $$h(\omega)=\begin{cases}f(\omega) \ \ \ \text{if} \ \ f(\omega)\in \mathbb{R} \\ \\ 0 \ \ \ \text{if} \ \ \ f(\omega)=\infty\end{cases}$$ How to show $h$ is measurable and $\int f d\mu = \int h d\mu?$ **Attempt:** It is known that the product of two...

I'm asked to evaluate the following integral: \int_{c} \frac{30z^2-23z+5}{(2z-1)^2(3z-1)}dz where c is the unit circle. This function has a simple pole at z=\frac{1}{3} and a second order pole at z=\frac{1}{2}, both of which are within my region of integration. I then went about computing the...

Homework Statement Homework Equations w=(2/3)x The Attempt at a Solution So integrating w to get V (1/3)x^2 +C Then Sum in the Y-direction should be 9-(2/3)x+18=0 Somebody tell me what in god's name is going on here. It seems like they are ignoring the 18kN force and then plugging in my...

Homework Statement Given that the circular arc wire with radius 'r' has a linear charge density ##\lambda##. What is the Electric field at the origin? Homework Equations ##\vec{E}=\frac{kq}{r^2}## where ##k=9\times10^9## is a constant. 3. The Attempt at a Solution I took a small segment dy...

Homework Statement Disk with radius R σ = M/A I = ∫ mr2 Homework Equations Today we learned how to derive various moments of inertia via density equations (M/L, M/A, M/V). I understand all of them except on how to get MR2/2 for a disk. The Attempt at a Solution I = ∫mr2 σ = M/A dM =...

Hi, I'm using KA Stroud 6th edition (for anyone with the same book, P407) and there is a example question where I just can't seem to get the answer they have suggested: Homework Statement [/B] Question: Determine the value of I = ∫(4x3-6x2-16x+4) dx when x = -2, given that at x = 3, I = -13...

Homework Statement Many places I have seen when solving integrals you change a lot of it into sums. http://math.stackexchange.com/questions/1005976/finding-int-0-pi-2-dfrac-tan-x1m2-tan2x-mathrmdx/1006076#1006076 Is just an example. So in general, how do you solve integrals (CLOSED FORM) by...

In the integral integral(1,infinity) e^(-sqrt(x)) / sqrt(x) STEP 1: I let u = -sqrt(x) du = -1/(2sqrt(x)) then my lower bound u = -1 then my upper bound u = -infinity -2 integral(-1,infinity) e^u du I would then switch the order of the integration bounds and multiply by -1My question is...

Hello, I have to compute the numerical integral of a function which is expressed at unequal (but almost) intervals. I tried the trapezoidal method, but the error is too large for my application. Is it possible to generalize the Boole's rule to or something on the same order of precision?

Mentor note: Thread was moved to homework section[/color] Hello Folks I have integral ∫0π/2 (sinx/sinx+cosx) dx I have got the answer is π/4 I have even solved indefinite integral [ln(tan^2(x/2)-2(tan(x/2))-1)]/2 + [tan-1(tan(x/2)) + [ln(1+tan^2(x/2))]/2]/2 my problem is I am not getting...

Hello, I am well aware of the ratio method, and the sum = 1/(1-r) but I want to try this method. I am trying to understand this: \displaystyle \sum_{n=1}^{\infty} e^{-n} using integrals, what I have though: = \displaystyle \lim_{m\to\infty} \sum_{n=1}^{m} e^{-n} = \displaystyle...

Does anyone know of a derivation or justification of Euler's substitution formulas for evaluating irrational expressions? In other words, to evaluate integrals of the form: \int R(x,\sqrt{ax^2+bx+c}) You can use Euler's substitutions: 1. \sqrt{ax^2+bx+c} = t \pm \sqrt{a}x, a>0 2...

Hi, everyone! I am trying to understand notation of this textbook http://arxiv.org/abs/hep-th/0108200 page 8, formulas 2.1.4 and 2.1.5 $$\int d \theta_\alpha \theta^\beta=\delta_\alpha^\beta$$ this could be found in any textbook the weird that from the above formula follows $$\int d^2...

Task in real analysis: P is a uniform partition on [0, π] and is divided into 6 equal subintervals. Show that the lower and upper riemann sums of sin (x) over P is lesser than 1.5 and larger than 2.4 respectively. My attempt at the solution: The greates value and the least value of sin x over...

http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas Simpson rule: 1 4 1, and the composite version: 1 4 2 4 2 4 2 4 ...4 1 in a double integral we just compute rows, and next columns, a this gives a matrix: http://mathfaculty.fullerton.edu/mathews/n2003/SimpsonsRule2DMod.html Milne's...

Basically, I'm modelling the flow of a "coating" process -- a fluid flow between a flat moving plane and a stationary cylinder, 2D, cartesian coordinates. Subscript 0 is the at the minimum height b/w the plane and the cylinder, and subscript c is at the point at which the flow leaves the moving...

In the integration of Force with respect to displacement (W=∫F.dx), is that true if the rate of change of displacement approaches to zero? My teacher said the one which approaches to zero is the rate of change of time. But If I arrange the formula, I will get F=dW/dx then F= lim Δx→0 ΔW/Δx...

Homework Statement A liter of air, initially at room temperature and atmospheric pressure, is heated at constant pressure until it doubles in volume. Calculate the increase in its entropy during this process. so Ti= 300K, Volume which is 2Vi=Vf; Pressure is constant Homework Equations ΔS...

Hi everyone! I would like to ask you for help with one of the tasks from my assignment. The rest of the assignment is done including some simple integration but I struggle with this one: Task "The total load capacity for a circular hydrostatic bearing is given as ##W=\int_0^{R_o} p_r(2πr dr) +...

Homework Statement Submerged (vertically) right triangle 12x9x15(hypotenuse) with 12 m leg parallel to water surface. Top of triangle is 3m below surface. Find force on triangle.[/B]Homework Equations I know mass of water is 840 k/m3. I think I should also multiply times 9.8 for gravity...

Homework Statement Let f(x1, x2, x3) = e-(x1+x2+x3), 0<x1,2,3<infinity, zero elsewhere be a joint pdf of X1, X2, X3. The variables are all independent to each other Compute P(X1< X2< X3|X3<1 ) Homework Equations P(X1< X2< X3|X3<1 ) The Attempt at a Solution P(X1< X2< X3|X3<1 )=P(X1< X2< X3<1...

I would like to solve an equation: NIntegrate[f[x],{x,a,b}]==1 For a and b, my function doesn't have analytic solution.

Hello everybody, apologies from outset for bad English. I wonder if anyone can give me some advice regarding my problem. I have a sesnor that gives acceleration readings. I have been working hard to turn these readings into position or displacements. I tried many method but MATLAB cumptrapz...

I'm still confused on some of these volume problems, so please bear with me :) Homework Statement Find the volume of a reentry spacecraft nose cone that has a cross-section radius of (1/4)x2 taken x feet from the nose and perpendicular to the axis of sym. We are given that the length of...

for the problem: \int {[(y-1)^3 + C]^{-1/2}}dy Is there a simple solution that can yield an answer? C is a constant. Integration by parts doesn't seem to look helpful (at least to me). Trigonometric substitution looks like one method that would work, though it would involve quite a bit of...

Hello everyone! I need some help with the integral: $\displaystyle \int \dfrac{1}{\tan^{-1}(x)}dx$ I don't know how to solve it... can you guys help me please?

Dear All, Can someone suggest me an appropriate routine (in Fortran) or command (in mathematica) to perform numerical integration of a function, which is specified numerically on a one dimensional grid with equal spacing (and we cannot generate additional data on other grid points)? There are...

Problem Show: \int_0^\infty \frac{cos(mx)}{4x^4+5x^2+1} dx= \frac{\pi}{6}(2e^{(-m/2)}-e^{-m}) for m>0 The attempt at a solution The general idea seems to be to replace cos(mx) with ##e^{imz}## and then use contour integration and residue theory to solve the integral. Let ##f(z) =...

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What is the difference between the measurable set-valued maps and measurable single-valued map? What is the difference between the integrable set-valued maps and integrable single-valued map? With illustrative examples, if possible? Thank you very.

Consider a pulley fixed to the ceiling. A mass-less string is wrapped around it, with each side of the string hanging down either side of the pulley. Since the pulley has friction with the string, tension along the string will vary. Let's say the string is attempting to move clockwise, so the...

Homework Statement Find the exact length of the curve: y= 1/4 x2-1/2 ln(x) where 1<=x<=2 Homework Equations Using the Length formula (Leibniz) given in my book, L=Int[a,b] sqrt(1+(dy/dx)2) I found derivative of f to be (x2-1)/2x does that look correct? The Attempt at a Solution I found f'...

Homework Statement Hello, I am to find the volume of the solid given by x2 + (y-1)2=1 rotated about the y-axis. I may use either shells or cylindrical method. I attempted shell method, but am just learning this, still foggy and this is the one question that isn't coming out right. Homework...

I am quite embarrassed to ask this question, as I know i have lost track of the concept here, but Ill nevertheless ask it. I was going through Mathematical methods for physicists (pg 333), and there was an example: "Solve $$y'+(1+\frac{y}{x}) = 0$$" My problem is, (a) when you put the...

Interestingly, I seem to have an integral I have posted before, but I want to take a different approach to it. $\int_{0}^{1} \frac{\ln(1+x)}{1+x^2} \,dx$ The beta function states, $B(x,y) = \int_{0}^{1} {t}^{x-1}({1-t}^{y-1}) \,dx$ So, I was just thinking if there a possible way to compute...

∫(x2 + 7x) cosx dx If I make v = (x2 + 7x) and du = cosx dx I get ((x2 + 7x) sinx)/2 If I make v = cosx and du = (x2 + 7x) dx I get ((x3/3 + 7x2/2) cosx)/2 using the form X=Y-X to X=Y/2 Neither are correct, what did I do wrong?

Hello, well here's my problem: I got this integral and I don't know how to calculate it (I am trying to find if there exists a k that satisfies this relation) : \int_0^k \frac{1}{ ( 4k-4r-2 ) ! ( 4r+1 ) ! }\, \left ( \frac{y}{x} \right )^{4r} dk = \int_0^k \frac{1}{ ( 4k-4r ) ! ( 4r+3 ) ! }\...

Homework Statement A exp( (− 3 R^2)/(2Na^2)) I wish to integrate ^ The expression is equal to P(N,R) The limits are infinity to -infinity. The intention is to find the normalisation constant / A in terms of N and a (then to cube it).The Attempt at a Solution This is what I've managed. A S...

Hi! Could someone please integrate the expression (with intention of finding the normalisation constant / value of A). Thanks a lot!

Hey! There is a question. Here is the integral: What I'm trying to do is starting with the third integral over zi and with the help of integral definition of DeltaFunction i want to calculate it. As you can see f(yi) has no influence on the integral. Am i right here?

Hello guys, since I am new at sums and multivariable calculus I faced a problem when I stumbled upon this: \sum_{r=0}^{k} \binom{n}{4r+1} x^{n-4r-1} y^{4r+1} = \sum_{r=0}^{b} \binom{n}{4r+3} x^{n-4r-3} y^{4r+3} Well, the problem is that I don't know if it's possible to put a limit in every...

Homework Statement Integrate (-m-kx)^-1 dx from a to b. The Attempt at a Solution So using the integral form I get the integral of (-m-kx)^-1 dx is (-1/k)*[ln(-m-kx)] with the bracketed expression being evaluated between a and b. (-1/k)*[ln(-m-ka) - ln(-m-kb)] My first...