# All Questions

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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 ...
35 views

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

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

### NIntegrate a singular function

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

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

Consider the following function: ...
475 views

### Speed up this NIntegrate

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

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] ...
78 views

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

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

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 ...
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 ...
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 ...
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 ...
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}] ...
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 ...
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 ...
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 ...
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 ...
74 views

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### 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): ...
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 ...
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 ...
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: ...
61 views

### Question regarding multidimensional integral

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