# All Questions

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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 ...
0answers
35 views

### High dimensional integral not evaluating? [duplicate]

I am trying to integrate as follows: ...
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 ...
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: ...
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.
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 ∞?
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 ...
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 ...
1answer
63 views

### NIntegrate a singular function

I am trying to do this integral numerically: ...
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] ...
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? ...
1answer
65 views

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

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

### Speed up this NIntegrate

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

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] ...
1answer
78 views

### Integrating only over positive values of an oscillating function

I have the following oscillatory function of time (it looks too lengthy!) ...
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: ...
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 ...
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 ...
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 ...
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'...
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 ...
1answer
49 views

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1answer
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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 ...
1answer
76 views

1answer
62 views

### Perform an explicit summation, if possible, over a restricted range of two indices both varying from 0 to infinity

I would like to sum the term ...
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 ...
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 ...
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 ...
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}] ...
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 ...
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 ...
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 ...
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 ...
1answer
74 views

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): ...
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 ...
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 ...
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: ...
0answers
61 views

### Question regarding multidimensional integral

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