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3
votes
1answer
51 views

Implementing Simpson's rule with two variables

For one of my lab project I need to integrate a given function (in this example, f1, using Simpson's ruls. When only one variable ...
0
votes
0answers
35 views

High dimensional integral not evaluating? [duplicate]

I am trying to integrate as follows: ...
0
votes
1answer
87 views

Performing a contour integration in Mathematica for a contour starting at $1$ and ending at $-\infty$ while avoiding the origin?

I would like to compute the following integral $I(k)$ in Mathematica to check if the result equals something I 'feel' is correct but I have no experience with contour integrals in Mathematica. I want ...
1
vote
0answers
45 views

Integration evaluation running forever

I am trying to integrate a function but the evaluation goes on and on forever. Here is the code: ...
0
votes
0answers
32 views

Why do I get the error message as integral does not converge?

Can anyone please help me to find the integral value of the following expression, Integrate[(x - t)^(-1), {t, 0, x}] It will be of a big help to me.
3
votes
1answer
72 views

Evaluating an integral combining a Bessel function with some other functions [closed]

How can I evaluate the integral of $j_1 ^2(x)\exp(-bx)/x$ from 0 to ∞?
2
votes
2answers
138 views

Compute unstable integral with high precision

I want to calculate $$ \int_{\mathbb{R}^n} e^{-t_1^4-t_2^4- ...-t_n^4-(1-t_1-t_2-...-t_n)^4} \text{d}t_1 \text{d}t_2 ... \text{d}t_n $$ with the highest possible n. I tried with ...
0
votes
1answer
64 views

Integrate a function of NDSolve

I'm having this problem of integrating a function that's the solution of a NDSolve multiplied by another function. I basically compute a cycle wich add at each step the quantity ...
1
vote
1answer
63 views

NIntegrate a singular function

I am trying to do this integral numerically: ...
1
vote
1answer
89 views

How to integrate exponent of sine?

I am trying to integrate Abs|E^ $\sin \theta$| (the absolute value of Euler's constant to the power of sin(theta), and tried the code Integrate[Abs[E^Sin[x]], x] ...
2
votes
1answer
75 views

Singular Integration

I am trying to simplify the following integral but getting no answer. Any help in how to get the resulting function as a function of t would be much appreciated? ...
1
vote
1answer
65 views

Very different results of NIntegrate using different methods: which one to believe

Consider the following function: ...
3
votes
2answers
475 views

Speed up this NIntegrate

Is there any trick to speed up this numerical integral: ...
0
votes
1answer
100 views

Numerical integration giving trouble

I am trying to do the following integral numerically, $$\rho(\theta_{j},\phi_{j})=\int\frac{\sin{\theta_{i}} d\theta_{i} d\phi_{i}}{\sqrt{2+2[\cos(\theta_{i})\cos(\theta_{j})+\sin{\theta_{i}\sin{\...
1
vote
1answer
61 views

How can I solve this integration or does it have a closed form solution?

The integral I am dealing with is below. I need to find the closed-form expression of this integral. $\int_0^\infty \ln(1+\frac{A}{1+B+Cx})\frac{e^{-x/M}}{M}dx$ Here, $A$, $B$, $C$ and $M$ are ...
3
votes
2answers
746 views

How to evaluate this function?

I’m trying to evaluate y[t] = InverseFunction[ NIntegrate[Sqrt[2]/( -8+Exp[y]+2Exp[-y]), {y,0,t}]] Some of the problems I’m facing, is that i’d like to get the ...
3
votes
3answers
103 views

Evaluating the error function by integrating $ \mathrm e^{−t^2} $ with Simpson's rule

I am trying to evaluate an error function with Simpson's rule because there is no other way to integrate it. The function is $$ {\rm erf}(x) = \frac{2}{\sqrt π}\int_0^x \mathrm e^{−t^2}\, \mathrm dt ...
2
votes
4answers
256 views

Integrating a list of values

The data given here data = Table[Clip[Sin[x], {0, 1}], {x, 0, 2 \[Pi], 0.1}] generates the following curve ListPlot[data] ...
1
vote
1answer
78 views

Integrating only over positive values of an oscillating function

I have the following oscillatory function of time (it looks too lengthy!) ...
1
vote
1answer
72 views

Why is my integral not being evaluated?

I am trying to integrate a function Gamma, but the output returns the input. I have the following code: ...
0
votes
0answers
65 views

Approximate/estimate the ratio of two multidimensional constrained integrals

I have a hypothesis that a certain "qubit-qutrit separability probability" should assume the value $\frac{5}{3} \left(112 \pi ^2-1105\right) \approx 0.659488$. In its initial formulation, this is a ...
2
votes
2answers
147 views

What is the fastest way of doing one integral in Mathematica?

I want to compute the following numerical integral in Mathematica $\int_0^L dy \int_0^y d \bar{y} f(y,\bar{y}),$ where $f(y,\bar{y})$ is a very complicated function. I show my code below where the ...
2
votes
1answer
69 views

How do I divide an integral into parts and sum the total?

I have an exercise looking like this: Analyze the integral $4\int_{0}^{1} \sqrt{1-x^2} \, \mathrm{d} x$ numerically by deviding the interval ${]0,1[}$ into three equal parts, then summarize the ...
1
vote
1answer
62 views

Midpoint Riemann Sum Code [duplicate]

I am trying to write a code in order to find the Riemann sum for the midpoint but can't seem to get the correct answer. I double checked what the answer should be but I haven't been able to find what'...
2
votes
0answers
96 views

Can this integral equation problem $\int_\Gamma \frac{e^{ik|x-y|}}{4\pi|x-y|}\varphi(y) \, \mathrm{d} y = u_{x_0}^{in}(x)$ be solved?

I am not sure if Mathematica is capable of solving integral equations in 2D/3D. I found this page in the documentation, but this is just for 1D. The following is what I would like to solve, it can ...
1
vote
2answers
146 views

Analytic or numerical integral calculation

I would like to integrate the following, $$f(x,y) = \frac{1}{(a - x)^2 + b (y-x^2)^2},$$ where $a>0$ and $b>0$ between definite bounds to obtain an analytic result ideally. I've tried the ...
2
votes
1answer
76 views

Does Mathematica have a 'nice' way to evaluate singular double integrals over line segments?

I want to perform a double integration over a line segment in 2D and I am wondering if can it be done in Mathematica. An added difficulty is that the integral is singular. $$I = \int_{(4,4)}^{(2,8)}\...
1
vote
1answer
109 views

Can Mathematica help me evaluate an integral over disjoint disks $I = \int_{D_1} \int_{D_2} \log|x-y| dy dx$?

I want to evaluate an integral that involves two disjoint unit disks $D_1$ and $D_2$. $D_1$ is centered at $(-2,0)$ and $D_2$ is centered at $(0,2)$. The integral I want to compute is $$I = \int_{D_1}...
0
votes
1answer
62 views
0
votes
0answers
55 views

Nested Cauchy type integration

I have a function which is in integral form: $$f_+(z)=\exp\bigg(\frac{1}{2\pi i}\oint_{C}\frac{f(\alpha)}{(z-\alpha)}\,d\alpha\bigg),$$ where $C$ is a unit circle. I want to take the Fourier ...
6
votes
2answers
180 views

Does Mathematica gives us a wrong result for the integral of a function including elliptic functions?

Calculus tells us that the differentiation of the integral of a function should be itself, but at least in one case Mathematica answers NO. I feel very confused. The new figure seems to bifurcate at ...
0
votes
2answers
287 views

Sum a certain hypergeometric-function-based expression pertaining to an integration problem

I would like to sum over the index $h$ from 3 to $\infty$, the expression ...
1
vote
1answer
71 views

Numerical solution to approximate the singular integration using collocation method

I am working to solve "numerically" the following integral equation IE: u[x]=f[x]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,x}]+Integrate[(1/(x-t)^(1/4))*u[t],{t,0,1}] ...
12
votes
1answer
320 views

Symbolic integration of potential over a disc : branch cut problem?

Context I am trying to explore the geometry of a crystal made of irregular bubbles. See animation here. very vaguely in the spirit of this post (it is in fact motivated by cosmology and galaxy ...
1
vote
1answer
57 views

Volume computation not returning expected result

I have tried to integrate the expression (0.5*(3*Cos[t]*Cos[t]-1))*(0.5*(3*Cos[t]*Cos[t]-1)) where t is in [0, π], as a ...
0
votes
1answer
88 views

Mathematica failing to compute function to calculate integral over a region bounded by straight line

Statement of the problem Consider the following situation: You have a model which employs a bivariate distribution with known parameters. You have a random realization from the distribution ...
0
votes
0answers
28 views

NIntegrate failed to perform the integration unless AdaptiveMonteCarlo method is chosen

I have multi-dimensional numerical integration of some function depending on one parameter. If no specification for the integration method is chosen, the output for specific values of the parameters ...
1
vote
1answer
74 views

How to apply NIntegrate two times?

I have following integration. $$I=\int_{0}^{\frac{\pi}{2}} \int_{0}^{\infty} \gamma e^{- \lambda \left(\gamma^2+2d\gamma\cos\theta -d^2 + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} 2d\cos\Theta(d\cos\...
1
vote
1answer
65 views

Evaluation of an integral using Mathematica

I am trying to evaluate the following integral, but the result I got is imaginary part. Do you know if there is a way to get a better evaluation of difficult integrals? ...
0
votes
1answer
95 views

Analytical form of the answer of a definite integral

I am trying to find out the analytical form of the answer of the following integration, $$I=\int_0^l r \, dr \int_0^{2\pi} \, d\phi (iks)[ \frac{\exp [ikx_0(N+r^2)^{1/2}]}{[x_0(N+r^2)^{1/2}]}\frac{\...
0
votes
1answer
34 views

Integrating a vector according to elements of another vector

I have two vectors, $\bar{x},\bar{v}$ and I want to produce a third vector such that:$$ u_i = \int_{x_i}^{x_i+\delta} f(v_i,t)dt \ .$$ I tried (with a simple function for example): ...
1
vote
2answers
165 views

Integration of a function that oscillates rapidly (apparently)

I would like to know if you could help me solve some doubts about the integration of a function that oscillates rapidly (apparently) that depends on time and two angular variables. The parameters S ...
0
votes
0answers
76 views

How to involve more cpu cores?

I'm working on Mathematica 11 (Lenovo Laptop, Core i7 cpu, 16GB Ram, SSD storage, windows 10 pro), part of my work is definite double integral, the evaluation time of this integral takes between 50 to ...
0
votes
0answers
286 views

An Issue with Numerical Evaluation of Coverage Probability

I am trying to numerically evaluate the following coverage probability expression: Here is my code: ...
0
votes
0answers
61 views

Question regarding multidimensional integral

I would like to compute the following iterated integral in 3 dimesions: $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \left|\int_{-\infty}^\infty f(y)f(y-t)e^{-i 2 \pi t \xi} dy\right|dt d\xi $$ ...
2
votes
0answers
69 views

Indefinite vs. definite integration contradiction in Version 11.3 [closed]

When evaluating the same integral using indefinite integration (method 1) or definite integration (method 2) I get different answers: method 1 = 0 and ...
1
vote
1answer
81 views

This complicated integral using numerical integration

I want to do the following integral $$ \int\limits_{-\pi/2}^{\pi/2}\dfrac{(k_{up}\cos\phi)\cdot(k_{down}\cos\alpha)}{k_{up}\cos\phi+k_{down}\cos\alpha}\cos{[(k_{up}\cos\phi-k_{down}\cos\alpha)x]}d\...
2
votes
1answer
151 views

NIntegrate: NumericQ and derivatives

I need to integrate a function with a singularity at the origin. I need this integration to happen quite fast, and while Integrate[] simply keeps on going forever, using NIntegrate with LocalAdaptive ...