Integration Definition and 1000 Threads

Homework Statement Given the graph of f(x) shown below, find the value of the integral. Photo attached. Homework Equations [/B] ∫23 5x·f(x2)dx The Attempt at a Solution [/B] I tried integration by parts to simplify the problem, but finding the integral of the composite function (f(x2))...

Greetings, I am desparately trying to solve a double integral via Monte Carlo integration. I integrate over two probability densities, the Beta distributions. Python can easily draw samples from these densities and calculate its function values. The integral can be seen here: Now my idea was...

Homework Statement find the Fourier transform of the following function in two ways , once using direct computation , and second using the convolution therom . Homework Equations Acos(w0t)/(d2+t2) The Attempt at a Solution I tried first to solve directly . used Euler's identity and got...

hi, I'm a high-school student that is just beginning to learn calculus. in calculus we are learning how to apply integration and diffrentiaiton methods regarding kinematics. there is this certain phrase i do not really understand in our textbook: e.g."in the second second" how am i meant to...

I have been looking everywhere for a clear explanation for the following: How do I know which way to integrate the electrical field, when I'm looking for the potential between to points? Example: I have to find the potential between the top conducting plate and the bottom conducting plate...

Homework Statement Show that $$\int_C e^zdz = 0$$ Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 +i and z = i. Homework Equations $$z = x + iy$$ The Attempt at a Solution I know that if a function is analytic/holomorphic on a domain and the contour lies...

Hi. Is it true to say that the integral over all volume of ∇ψ where ψ is a scalar function of position and time is just ψ ? Thanks

Homework Statement I want to compute ##I=\int_C \dfrac{e^{i \pi z^2}}{sin(\pi z)}##, where C is the path in the attached figure (See below). I want to compute this by converting the integral to one whose integration variable is real.Homework Equations There are not more relevant equations. The...

Homework Statement I want to integrate ∫-e^(2x)*sin(e^x) dx Homework Equations ∫uv'dx=uv - ∫u'v The Attempt at a Solution u = e^2x du = 2*e^2x dv = sin(e^x) v = -cos(e^x)/e^x e^(x)*cos(e^x) - 2∫e^(x)*cos(e^x) dx e^(x)*cos(e^x) - 2*sin(e^x) + c The solution I have doesn't have the two in...

Homework Statement Homework Equations F=ma F/m = a The Attempt at a Solution Fc = constant force fquad= cv'^2 [/B] (Fc-cv'^2)/m = a (Fc-cv'^2)/m = dv' / dt' * using the primes to differentiate between v and v' during integration dt '(Fc-cv'^2) dv'*(m) dt' = (m/ (Fc-cv'^2)) dv' dt'...

Hi. I came across the following integral in contour integration lim(ε→0) "integral of" exp(iaεeiθ) dθ = θ If I take the limit first then it just becomes the integral of 1 which is θ. I have 2 questions - If I take the limit first and then perform the integral do I always get the same answer as...

When doing integration such as \int_{0}^{2\pi} \hat{\rho} d\phi which would give us 2\pi \hat{\rho} , must we decompose \hat{ρ} into sin(\phi) \hat{i} + cos(\phi) \hat{j} , then \int_{0}^{2\pi} (sin(\phi) \hat{i} + cos(\phi)\hat{j}) d\phi , which would give us 0 instead? Thanks

I have values for the variables (C, v, g, w at all sample points) but I do not know how to evaluate the integral. This equation is supposed to be implemented on a computer as part of a larger algorithm for navigation purposes. I have a feeling that the gyroscope sensor reading and or the...

Homework Statement I wish to solve this integral $$b_{lm}(k) = \frac{1}{2(\hbar)^{9/4}(2\pi)^{5/2}\sqrt{\sigma_{px} \sigma_{py} \sigma_{pz}}} \int_{\theta_k = 0}^{\pi}\int_{\varphi_k = 0}^{2\pi} i^l \text{exp}\left[ - \frac{1}{(2\hbar)^2}\left(\frac{(k_z - k_{z0})^2}{\sigma_{pz}^2} + \frac{(k_y...

Hi everyone, So I am a high school student and I am learning calculus by myself right now (pretty new to that stuff still). Currently I am working through some problems where integration leads to logarithm functions. While doing one of the exercises I noticed one thing I don't understand. I...

I want to find the numerical solution to the following nested integral in Python \frac{K!}{(K-M)!}\int_{x_1=0}^{y}\int_{x_{2}=x_1}^{\max(x_1,\,y-x_1)}\cdots \int_{x_M=x_{M-1}}^{\max(x_{M-1},\,y-\sum_{m=1}^{M-1}x_m)} \frac{1}{(1+x_M)^{K-M+2}}\prod_{m=1}^{M-1}...

What does the author want to say through these lines? What is the *harm* he is talking about? I will be thankful for any help!

Homework Statement I am trying to calculate the contour integral of the complex conjugate of z around a square with sides of length 2 centred on the origin in the complex plane Homework Equations ∫ f(z) dz = ∫ f(t) (dz/dt) dt . It looks like the integral signs won't appear here but...

Homework Statement find integral of the function- (x^2 + cos^2)(cosec^2) / (1+x^2) 2. The attempt at a solution I noticed the denominator is the derivative of Arctan(x), I tried integrating by parts with various choices for 1st and second function but all of them end up being more complicated...

Homework Statement ∫1/(√3 sinx+ cosx) dx is Ans. as per textbook 1/2(log(tan((x/2)+(pi/12)) 2. The attempt at a solution Attempt 1-I changed it to half angles (x/2) and then multiplied and divided sec^2(x/2) to the numerator and denominator, then putting tan(x/2)=t I got 2∫1/(√3t+1-t^2) I wrote...

Homework Statement Find ∫sqroot((cosx-cos^3(x))/(1-cos^3(x))) 2. The attempt at a solution I tried taking cosx common on top which gives cosxsin^2(x), but it didn't give me any benefit, I tried splitting the numerator, factoring in sec^2(x) and a bunch of substitutions to no avail. Finally...

Homework Statement if f(x)= lim(n→∞) e^(xtan(1/n)log(1/n)) and ∫f(x)/(sin^11x.cosx)^1/3 dx=g(x)+c, then 1) g(pi/4)=3/2 2) g(x) is continuous for all x 3) g(pi/4)= -15/8 4) g(pi/4)=12 2. The attempt at a solution Part a-Evaluating the limit, since 1/n tends to 0, log(1/n)→-∞=-n, using...

Homework Statement If the derivative of f(x) w.r.t x is (0.5- sin^2x)/f(x) then fundamental period of f(x) is 2. The attempt at a solution I wrote 1/2-sin^2x as cos2x/2. since f'(x)=cos2x/2f(x) its integral will be f(x), I would be grateful is someone could provide intuition on how to proceed...

Homework Statement ∫e^(-x)(1-tanx)secx dx 2. Attempt at a solution I know ∫e^x(f(x)+f'(x))=e^x f(x) and I intuitively know f(x) could be secx here and therefore f'(x) will be secxtanx but I can't figure out how to reach that

Homework Statement ∫(√x)^5/((√x)^7+x^6) dx Homework Equations I have learned integration through substitution, trigonometric identities and standard integrals The Attempt at a Solution I took (√x)^5 common which gave 1/(x+√x^7), Then I tried to substitute √x=t, √x^7=t but it just seems to...

Homework Statement The value of ∫{[x]}dx (where {} and [] denotes the fractional part of x and greatest integer function) 1) 0 2) 1 3) 2 4)all are correct 2. The attempt at a solution Since [x] is always an integer, the given function will always have a value=0. I thought that since the...

Homework Statement Apologies if this is obvious, maybe I'm a little out of touch ## \int\limits^b_0 \frac{x^3}{x^2+m^2} dx ## Homework EquationsThe Attempt at a Solution I [/B]was going to go by parts breaking the ##x^3 = x^2 . x## So that I have the logarithm I.e : ##b^2 \frac{log (b^2...

In this super short video of the derivation of the relativistic kinetic energy, , I'm just stuck on one thing. Around 1:00 minute in, the constants of integration change from 0 to pv when the integration changes from dx to dv. Where does the pv come from? Thanks!

I am reading Spacetime and Geometry by Sean Carroll. In section 1.10 on classical field theory, he uses this formula (1.132) The curly L is a Lagrange density. S is an action, Φ is a vector potential. Could the integral also be written as follows?

Homework Statement is dx/dy= x/y if yes can i use it always Homework Equations for example in a circle dA/dtheta=A/360The Attempt at a Solution if its right sometimes what are the conditions of using it

How to Integrate it::: ∫e^(ax²+bx+c)dx Or in general e raised to quadratic or any polynomial. I am trying hard to recall but I couldn't recall this integration. I tried using By-parts but the integration goes on and on.

Homework Statement Real atomic nuclei are not point charges, but can be approximated as a spherical distribution with radius ##R##, giving the potential $$ \phi(r) = \begin{cases} \frac{Ze}{R}(\frac{3}{2}-\frac{1}{2}\frac{r^2}{R^2}) &\quad r<R\\ \frac{Ze}{r} &\quad r>R \\...

I have the integral ##\displaystyle \int_0^{2 \pi} \frac{1-\cos x}{3+\cos x} ~ dx##. I want to make the tangent half-angle substitution ##t = \tan (x/2)## so that I can get a rational function. However, both limits of integration just become zero. This is the first case. In the second case, I...

I"ve seen several texts that say something like this: Our equation of motion along x is dvx/dt = -g(vx/vt) Integrating this, we obtain equation 178 at this link (pretty near the top; sorry, but I can't figure out how to put the equation here). It's from FitzPatrick's online notes for...

Here's what I have to do: 1) I arbitrary give a first value to the variable ##x_b##. Let's say ##x^{(0)}_b = 0.3## 2) I find ##x_D## by evaluating this integral: $$ln(\frac {52.32} {100}) = \int_{0.5}^{x^{(0)}_b} \frac {dx} {x^{(0)}_D - x}$$ 3) I use the value I got for ## x^{(0)}_D## to...

Where is it useful?

Hi, I am trying to evaluate the following integral numerically in MATLAB \int_0^{\infty}\frac{e^{-jt}E_1^2(-jt)}{t}\,dt where ##j=\sqrt{-1}##, and ##E_1(x)## is the exponential integral. My code is fun = @(x) (exp(-1i*x).*(expint(-1i*x)).^2)./x; q = integral(fun,0,Inf) but I get the...

In definite Integration simply we find out the area under the curve.If I am not wrong the processing is like that we divide the area in infinite numbers of rectangles and then find out the summation of all rectangles area. My Question is here, how it is possible to add infinity? assume you have...

Homework Statement Please help me solve the calc problem pictured! Homework Equations y=3-x^2 and y=x+1 The Attempt at a Solution My attempt is in one of the photos!

Homework Statement Please look at the photo! Homework Equations -x^2+4x=x^2-6x+5 The Attempt at a Solution I got 2x^2-10x+5 but it says it's wrong

here is a link with the formula: https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms.pdf i'm talking about the formula that says the integral of f'(x)/f(x)dx = ln(f(x))+C it's kind of hard to put this into Google. where does this formula...

Hello, Is this integral solvable in compact form? \int_0^{\infty}e^{-j\nu\alpha}E_1^m(-j\nu)\,d\nu where ##E_1(.)## is the exponential integral and ##j=\sqrt{-1}##. I am trying to avoid solving it numerically because its solution won't be the end result. Thanks

I have the pdf of a random variable found from the characteristic function given by f_X(\alpha)=\frac{1}{2\pi}\sum_{m=0}^Mj^m{K\choose m}\int_0^{\infty}e^{-jt(m+\alpha)}E_1^m(-jt)\,dt where ##j=\sqrt{-1}## and ##E_1(x)## is the exponential integral. I need to find the CDF of the random...

One of my students ask me: "Which axioms are the basic of the integration?" What I should answer him? Any ideas?

I have seen two approaches to the method of integration by substitution (in two different books). On searching the internet i came to know that Approach I is known as the method of integration by direct substitution whereas Approach II is known as the method of integration by indirect...

Homework Statement ∫ e1000((sinx)/x) dx [0 to 1000 : bound of integration]. Solve this integral of a sharply peaked function without a calculator. Homework Equations I'm doing this in relation to statistical thermodynamics - I think I need to use Sterling's Approximation or a gamma function...

Homework Statement $$f(x)=NormalPDF(x,2,1)+NormalPDF(x,2,(1/2)^2)$$. where NormalPDF(a,b) is the PDF for a normal distribution with mean a and variance b. Use Monte Carlo Integratoion to find: $$\int_{-10}^{10}f(x)dx$$ Homework Equations The solution to this integration is 2. I use the method...

Homework Statement Show that \int_{A} 1 = \int_{T(A)} 1 given A is an arbitrary region in R^n (not necessarily a rectangle) and T is a translation in R^n. Homework Equations Normally we find Riemann integrals by creating a rectangle R that includes A and set the function to be zero when x...

Homework Statement in the picture. Homework Equations F=ILcrossB Along with the original question, the other picture contains the solution with different numbers. I was just wondering why when finding the force on the wire instead of making dl= R*dtheta and going through the integration and...

Hi, I am reading "An Introduction of Solid State Physics" from Ibach Lüth and don't understand the integration process. They write $$\sigma=\frac{e^2}{8\pi^3 \hbar} \int df_{E}dE \frac{v^2_x(\bf{k})}{v(\bf{k})} \tau(\bf{k}) \delta(E-E_F) $$ $$ = \int_{E=E_F}^{}df_{E}...