Integral Definition and 1000 Threads

From the path integral approach, we know that ## \displaystyle \langle x,t|x_i,0\rangle \propto \int_{\xi(0)=x_i}^{\xi(t_f)=x} D\xi(t) \ e^{iS[\xi]}##. Now, using ## |x,t\rangle=e^{-iHt}|x,0\rangle ##, ## |y\rangle\equiv |y,0\rangle ## and ## \sum_b |\phi_b\rangle\langle \phi_b|=1 ## where ## \{...

I have this problem with a complex integral and I'm having a lot of difficulty solving it: Show that for R and U both greater than 2a, \exists C > 0, independent of R,U,k and a, such that $$\int_{L_{-R,U}\cup L_{R,U}} \lvert f(z)\rvert\,\lvert dz\rvert \leqslant \frac{C}{kR}.$$ Where a > 0, k...

Homework Statement Let ##f(x,y)=(xy,y)## and ##\gamma:[0,2\pi]\rightarrowℝ^2##,##\gamma(t)=(r\cos(t),r\sin(t))##, ##r>0##. Calculate ##\int_\gamma{f{\cdot}d\gamma}##. Homework EquationsThe Attempt at a Solution The answer is 0. Here's my work. However, this method requires that you are...

Homework Statement I am having question with part c , for both c1 and c2 , here's my working for c1 , i didnt get the ans though . My ans is -5 , but the given ans for c1 and c2 is 27 , is the ans wrong ? Or which part i did wrongly ? Homework EquationsThe Attempt at a Solution

Hello. I have a difficulty to understand the branch cut introduced to solve this integral. \int_{ - \infty }^\infty {dp\left[ {p{e^{ip\left| x \right|}}{e^{ - it\sqrt {{p^2} + {m^2}} }}} \right]} here p is a magnitude of the 3-dimensional momentum of a particle, x and t are space and time...

$\int_{3}^{\infty} \frac{1}{\sqrt{x} - 1} \,dx$ I need to find if this converges or diverges. I'm trying u-substitution, so $u = \sqrt{x} - 1$. Therefore, $du = \frac{1}{2\sqrt{x}} dx$. I'm not sure how to proceed from here.

Homework Statement Find the solution of the following integral Homework Equations The Attempt at a Solution I applied the above relations getting that Then I was able to factor the function inside the integral getting that From here I should be able to get a solution by simply finding the...

I assume this is a simple summation of the normal components of the vector fields at the given points multiplied by dA which in this case would be 1/4. This is not being accepted as the correct answer. Not sure where I am going wrong. My textbook doesn't discuss estimating surface integrals...

Evaluation of $\displaystyle \int^{\frac{1}{2}}_{0}\frac{1}{(1-2x^2)\sqrt{1-x}}dx$ $\bf{Try::}$ Let $\displaystyle I = \int^{\frac{1}{2}}_{0}\frac{1}{(1-2x^2)\sqrt{1-x}}dx$ Put $1-x=t^2\;,$ Then $dx=-2tdt$ So $\displaystyle I = \int^{1}_{\frac{1}{2}}\frac{2t}{\left[1-2(1-t^2)^2\right]t}dt =...

Please anyone can help solve this integral equation e^t+e^t ∫ (t, 0 ) e^(-τ) x f(τ) dτ

I know integral of (2x+1)/(x^2+x). but i don't know integral of (x^2+x)/(2x+1). I'm very curious... please answer me...

Sorry where is pi/4 coming from in the line integral(section 3)? because i think it should be 1/2=tan(theta) which theta is 26.5651... it is impossible that the angle is pi/4? where is pi/4 coming from inside the circle? thank

Homework Statement Sorry that I am not up on latex yet, but will describe the problem the best I can. On the interval of a=1 to b= 4 for X. ∫√5/√x. Homework EquationsThe Attempt at a Solution My text indicates the answer is 2√5. I have taken my anti derivative and plugged in b and subtracted...

Homework Statement No actual work, could just use some assistance in understanding formulas involving the centroid of an object, specifically with integrals. For example, how would you understand the following formula(s) (as seen in part 2)? I understand that the centroid is the sum of all the...

I have $$\int_{}^{} \frac{1}{\sqrt{1 - x^2}} \,dx$$ I can let $x = \sin\left({\theta}\right)$ then $dx = cos(\theta) d\theta$ then: $$\int_{}^{} \frac{cos(\theta) d\theta}{\sqrt{1 - (\sin\left({\theta}\right))^2}}$$ Using the trig identity $1 - sin^2\theta = cos^2\theta$, I can simplify...

Homework Statement Transform given integral in Cartesian coordinates to one in polar coordinates and evaluate polar integral. ##\int_{0}^3 \int_{0}^x \frac {dydx}{\sqrt(x^2+y^2)}## Homework EquationsThe Attempt at a Solution I drew out the region in the ##xy## plane and I know that ##0 \leq...

Hello I have tried gaussian integrals does gaussian integrals have this general form formula? if not then weather i do integration by parts or what just needed a hint to solve it correctly

Homework Statement I'm having some trouble evaluating the integral $$\int^\infty_{-\infty} \frac{\sqrt{2a}}{\sqrt{\pi}}e^{-2ax^2}e^{-ikx}dx$$ Where a and k are positive constants Homework Equations I've been given the following integral results which may be of help $$\int^\infty_{-\infty}...

If a brick is pulled across the floor by a rope thruogh a pulley, 1 meter above the ground - and work = W, where W = 10N , (in Newton).Show that the horizontal component of W, which is pulling the brick has the size \frac{10x}{\sqrt{1+x^2}} (*) Use this to calculate the amount of work needed...

Homework Statement A 12 foot light pole stands at the corner of an 8 foot by 10 foot rectangular picnic blanket spread out on the ground. A bee flies in a straight line from a point P on the pole to a point Q on the blanket. Set up a multiple integral whose value represents the average length...

This is my first time using this site so please excuse me if I missed any guidelines. 1. Homework Statement A plastic rod having a uniformly distributed charge Q=-25.6pC has been bent into a circular arc of radius R=3.71cm and central angle ∅=120°. With V=0 at infinity, what is the electric...

I am trying to evaluate the following integral. ##\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1## How do you do the integral above?

Homework Statement $$f(x,y,z)=y$$ ; W is the region bounded by the plane ##x+y+z=2##, the cylinder ##x^2 +z^2=1##, and ##y=0##. Homework EquationsThe Attempt at a Solution Since there is a plane of ##y=0##, I decided that my inner integral will be ##y=0## and ##y=2-x-z##. But after this I have...

So, ∫x/(1-x)... can I solve this as a power series ∫(x*Σ x^n) = ∫(Σ x^(n+1))= (1/(n+2)*Σ x^(n+2))? Is this correct? I know there is other ways to do it... But should this be correct on a test? This solution is more fun..

Is it possible to do an integral of f(x)*x without knowing f(x)?

Homework Statement Determine ##\int_{0}^{2}\sqrt{x}dx## using left riemann sums Homework Equations ##\int_{a}^{b}f(x)dx = \lim_{n\rightarrow \infty}\sum_{i=0}^{n-1}(\frac{b-a}{n})f(x_i)## The Attempt at a Solution [/B] ##\frac{b-a}{n}=\frac{2-0}{n}=\frac{2}{n}## ##\int_{0}^{2}\sqrt{x}dx =...

Hi, what kind if integration used on equation 1 so it turned into equation 2? this does not look like integration by parts. and where (x-x0) appeared from instead of (k-k0) ? thanks for your help.

Consider the definite integral ∫202x(4−x2)1/5 dx. What is the substitution to use? u= 4-x^2 Preview Change entry mode (There can be more than one valid substitution; give the one that is the most efficient.) For this correct choice, du/dx= -2x Preview Change entry mode If we make this...

[Question] So I was thinking about Physics for some time and for the sake of curiosity I've came with this problem: Let's say we have a liquid flowing into a system with infinite space. The flow is constant ( F ) The liquid decays over time with a half life ( λ ) We're looking for the Total...

Homework Statement Evaluate the following integral: ∫0∞ √(x)* e-x dx Homework Equations ∫0∞ e-x2 dx = (√π)/2 The Attempt at a Solution So far this is what I've done: u = x1/2 du = 1/2 x-1/2 2 ∫ e-u2 u2 du Now, I'm not really sure what to do? Or if what I've done so far is leading me down...

I'm going through the book "Elementry Differnetial Equations With Boundary Value Problems" 4th Eddition by William R. Derrick and Stanley I. Grossman. On Page 138 (below) ) The authors take the derivative of a definite integral and end up with a definite integral plus another term. How did...

Is this question correct? We are given to evaluate: $$\int_0^2 \left(e^x-e^{-x}\right)^2\,dx$$ $$2\left(\frac{1}{2}\sinh(x)-x\right)$$ $$2\left(\frac{1}{2}\sinh(2\cdot2)-2\right)-2\left(\frac{1}{2}\sinh(2\cdot0)-0\right)$$ $$\sinh(4)-4$$

Hello, I need some help finding the integral $\int_{0}^{1}x\sqrt{18-2x^2} \,dx$ Let $u= 18-2x^2$ $du=-4xdx$ $-1/4 \int_{16}^{18} \sqrt{u} \,du$= $36 sqrt(2) -128/3$ I am getting the wrong solution: $9\sqrt(2)-32/3$

Homework Statement Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinders: y = 1 − x2, y = x2 − 1 and the planes: x + y + z = 2 4x + 5y − z + 20 = 0 Homework Equations ∫∫f(x,y) dA The Attempt at a Solution So I solved for z in the plane...

Hi, I am stuck on this question and was wondering if anyone could help me. The topic is integral equations. A block of land is bounded by two fences running North-South 5 km apart a fence line which is approximated by the function N=0.5E and a road which is approximated by the curve...

Hi everyone. I have quite a basic doubt, and I thought you could help me. Consider the figure: The cylinders S1 is held at a constant potential, and the same applies for the ring identified by S0. All the surroundings are filled with an insulator material. I want to calculate che capacitance...

Homework Statement Find the volume of the given solid: Under the surface z = xy and above the triangle with verticies (1,1), (4,1) and (1,.2) Homework Equations Double Integral The Attempt at a Solution I drew the triangle, and found the the equations of the lines to be: x = 1; y = 1; y = -3x...

Homework Statement Let ##f(t)=\int_{t}^{t^2} \frac{1}{s+\sin{s}}ds,t>1.##Express ##f## as a composition of two differentiable functions ##g:ℝ→ℝ^2## and ##h:ℝ^2→ℝ##. In addition, find the derivative of ##f## (using the composition). Homework EquationsThe Attempt at a Solution Honestly, I have...

Homework Statement $$\int \tanh=?$$ Homework Equations $$\cosh^2-\sinh^2=1$$ $$(\tanh)'={\rm sech}^2=\frac{1}{\cosh^2},~~(\coth)'=-{\rm csch}^2=-\frac{1}{\sinh^2}$$ $$({\rm sech})'=\left( \frac{1}{\cosh} \right)'=-{\rm sech}\cdot\tanh=-\frac{\sinh}{{\rm cosh}^2}$$ $$({\rm csch})'=\left(...

Hello good evening to all, I was studying here and got stuck with this. I solved the integral and got [x+sin(x) -1] and that´s the farthest that I got. I would appreciate the help.

Homework Statement I'm just required to setup the integral for the question posted below Homework EquationsThe Attempt at a Solution So solving for phi @ the intersection of the sphere and the plane z=2: z = pcos(phi) 2 = 3cos(phi) phi = arccos(2/3) so my limits for phi would go from 0 to...

Homework Statement Solve for the solution of the differential equation and use the method of variation of parameters. x`` - x = (e^t) + t Homework Equations [/B] W= (y2`y1)-(y2y1`) v1 = integral of ( g(t) (y1) ) / W v2 = integral of ( g(t) (y2) ) / W The Attempt at a Solution [/B] yc= c1...

Hey everyone, I am trying to evaluate the following integral: \int z(z+1)cosh(1/z) dz with a C of |z| = 1. Can someone please guide me with how to start? I have tried to parametrise the integral in terms of t so that z(t) = e^it however the algebra doesn't seem to work...

Homework Statement Consider the 'ice cream cone' bounded by z = 14 − x2 − y2 and z = x2 + y2 .(a) Find the equation of the intersection of the two surfaces in terms of x and y. (b) Set up the integral in polar coordinates. Homework EquationsThe Attempt at a Solution I got part a without...

Hello All! I am trying to solve the simple pendulum without using a small angle approximation. But I end up with this integral: $$\int_{\frac{\pi}{4}}^{\theta}\frac{d\theta}{\sqrt{cos(\theta)-\frac{\sqrt{2}}{2}}}$$ Is this possible to evaluate? If so, could I get a hint about what methods to...

Suppose ##\intop_{-\infty}^{+\infty}(f(x))^{2}dx=1##, and ##a=\intop_{-\infty}^{+\infty}(\frac{df(x)}{dx})^{2}dx##, does a maximum value of ##a## exist? If it exists, what's the corresponding ##f(x)##?

Hello. I'm new to physics, and the problem I have seems so basic, mathematically speaking. I'm just failing to grasp exactly what is being asked. If I can find that, I believe I can find the answer. Here it is: 1. Homework Statement Let A = x2ˆx + y2ˆy + z2ˆz Consider the parabolic path y2 =...

http://‪C:\Users\johny\Downloads\q4.jpg 1. Homework Statement Hi, so the question is I have to tell if this integral diverges or converges.(without solving it) integral(1/(e^x sqrt(x)))dx from 1 to +inf Homework Equations integration techniques. The Attempt at a Solution my answer: let 1/e^x...

Homework Statement Prove that ##\int _0^a\left(\frac{f\left((sin(ln(c))x\right)+\sqrt{\cos \left(e-\pi ^2\right)}}{\ln \left(\pi ^2-e\right)+\pi ^2\sqrt{\cos \left(e-\pi ^2\right)}}\right)dx## is a probability density function (when ##a=\frac{1}{\pi ^2}##) given that ##\int _0^{\pi...

doubt in this fraction in here Because he, simplify 12 with 4 ?? do not understand! someone could make another example ,with fraction ! Thank you!