Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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0
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1answer
45 views

how can use $\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$ [on hold]

How can calcul $$\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$$
0
votes
0answers
45 views

Mathematica can't, or won't evaluate an integral (again)

I'm relatively new to Mathematica and really need some help here to spot what's going wrong with my integration issues; Mathematica doesn't evaluate my integral, after a fair amount of time running, ...
0
votes
1answer
46 views

How to make Mathematica show intermediate steps in integral [duplicate]

I want to know how Mathematica evaluates this integral: $PV \int _ {0} ^ {i \infty} d \tau \, \frac{e^{-\frac{\tau^2}{2 M^2}}(b^2 - 3 τ^2)^2 (|b^2+\tau^2|-(b^2-\tau^2))}{\tau (\tau^2 - b^2)}$, where ...
0
votes
1answer
81 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
0
votes
1answer
29 views

Function to Represent Recursive Integral

I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$): $K_{i,n}\left(x\right)=\intop_{x}^{\infty}K_{i,n-1}\left(y\right)dy$ where ...
0
votes
3answers
72 views

Why does FindMinimum return 'The function value Null is not a real number'?

I am working with the following function ...
3
votes
1answer
119 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
0
votes
1answer
33 views

Integration with changing parameter [on hold]

I want to calculate the integral of Rev for a = 0 to 1 by step 0.1. How can I do it? ...
1
vote
0answers
54 views

Calculate exact Probability of product of normal random variables

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = ...
2
votes
0answers
39 views

Getting error messages from a Plot expression containing an integral [closed]

This should be a really simple question, but I just got confused. Plot[Integrate[x, x], {x, -5, 5}] Integrate::ilim: Invalid integration variable or limit(s) ...
0
votes
0answers
23 views

Taking a multi-dimensional residue [on hold]

Consider the function ...
-1
votes
1answer
66 views

Help me with sum [closed]

good morning $$ \begin{array}{l} \left\{ \begin{array}{l} u_0 = 1 \\ u_n = 3 - \frac{4}{{1 - v_n }} \\ \end{array} \right.\quad \\ \;v_n = \left( { - 3} \right)^{n + 1} \\ s = v_{1436} ...
3
votes
2answers
129 views

Integral does not converge (when it should)

I was looking at integrals like: Integrate[HermiteH[50, x]*Exp[-x^2], {x, 0, Infinity}] which gave me a "does not converge on $(0,\infty)$" error. On the other ...
0
votes
1answer
58 views
0
votes
1answer
59 views

Integrating spherical harmonics

I am trying to simply check the integration/normalization condition on the SperhicalHarmonic functions that are built into Mathematica. So basically, I just want to check that the following integral ...
2
votes
1answer
56 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
1
vote
1answer
44 views

Performance boost for definite integration with symbolic limits

In Mathematica, the symbolic definite integration ...
2
votes
0answers
68 views

How can I do multiple (double) integral with periodic boundary conditions?

I am trying to do a simple double integral $\int_0^l \left[\int_0^l h^3 h_{xxx}dx\right]dx$ with periodic boundary conditions $h[0,\tau]=h[l,\tau]$ $h_x[0,\tau]=h_x[l,\tau]$ ...
0
votes
0answers
6 views

Does anyone know names of some of Newton's THEOREM? [migrated]

Does anyone know names of some of Newton's THEOREM? any or a list of them would be great. I already know about the Shell method.
0
votes
2answers
54 views

Derivative after numerical Integration

So I have a function that I want to numerically integrate with respect to temperature, so the integral changes depending on the value of temperature being used as it is one of the bounds. After ...
2
votes
1answer
74 views

Limits and transformation rules

I can calculate this limit: Limit[(c^(1 - g) - 1)/(1 - g), g -> 1] and obtain the correct value: Log[c] but if I try ...
0
votes
2answers
116 views

What is the simplest way to plot x^(1/3) on the interval [-3,3]?

My question is: What is the simplest way to plot x^(1/3) on the interval [-3,3]?
1
vote
1answer
78 views

How to avoid complex terms in the results given by Integrate?

As shown by In1, integrating Sqrt[x^2 - 1]/(a + x^2) (1/x) returns a result with a complex terms; however, after I make a ...
2
votes
0answers
53 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
0
votes
1answer
100 views

Writing a Code to plot a function that includes a double integral [closed]

I am trying to write a code in Mathematica. Here are my steps: F[u_] = Some nontrivial and long expression in terms of u; Umax[x_, y_] = Some expression in terms of x and y; W[x_, y_] := integral ...
6
votes
1answer
190 views

Incorrect evaluation of integral involving a DiracDelta, whose argument has infinitely many zeros

Let's say $X>0$ is a random variable with probability density $p_X(x)={\rm e}^{-x}$. Define the random variable $Y=\sin(X)$. From the transformation theorem for probabilities we know that its ...
1
vote
1answer
77 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
1
vote
2answers
57 views

Integrating a compound expression

I have an integral of the form I[r]=∫(arExp[-r]-brSin[k(r-d)]Exp[-r])BesselJ[0,kr]dr where Besse1J[0,kr] is the modified ...
2
votes
1answer
126 views

Inverse gradient operator

I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the ...
1
vote
1answer
92 views

Mathematica is able to compute an indefinite integral but not the corresponding definite one

I'm trying to compute the following definite integral (μ is a parameter): ...
4
votes
2answers
299 views

Probability: Calculating a multiple integral

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=2,5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Cauchy Distribution having location parameter $\mu_{10\times 1} = ...
5
votes
3answers
365 views

Bug in complicated Limit

The code Limit[Log[2 - Sin[x]*Cos[x]], x -> Infinity] outputs Interval[{0, Log[3]}] in Mathematica 10.0.2.0 . It should ...
3
votes
2answers
483 views

Color a Function by its Derivative

Mathematica's ColorFunction seems to struggle with coloring a function "y" by its derivative D[y,x]. This is a seemingly simple task, but Mathematica can't handle it. While I can certainly evaluate ...
0
votes
1answer
55 views

Integration of an expression yields wrong result

I'm trying to find a general expression for the definite integral of ...
2
votes
2answers
236 views

After definite integration the result is still integration variable dependent!

This integral $\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\frac{\exp \left(\frac{2}{x^2+y^2+z^2+1}-2\right)}{\left(x^2+y^2+z^2+1\right)^4}dzdydx$ or ...
-4
votes
1answer
63 views

NDSolve a differential equation depending on some parameter

I have to solve the differential equation, to get a plot of T and R, ...
2
votes
1answer
181 views

Calculating the area under a curve

How can I calculate the area under a curve after plotting discrete data as per below? ...
1
vote
3answers
85 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
0
votes
1answer
55 views

Derivatives of overscript variables

If we have an expression with terms of some variable and terms of the same variable with some overscript, the differentiation of this expression does not entirely function. The problem is that ...
-1
votes
1answer
139 views
3
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2answers
91 views

Integration of a Rational Function returns RootSum[]

I am trying to solve an integral given below: Integrate[r^2/(-α r^3 + r^2 - 2 m r + Q^2), r] but since coefficients of this cubic polynomial are as parameters, ...
7
votes
2answers
263 views

Definite integral incorrectly giving a nonreal value

In Mathematica 10.0, when I enter N[Integrate[Sqrt[1+x^3],{x,-1,3}]] , I get a nonreal value. (I.e., the imaginary part is nonzero.) Why? This arose when I ...
0
votes
2answers
79 views

A simple integral operation

Evaluating the following expression results in a non-zero output FullSimplify[Integrate[2 f[x], {x,0,1}] - 2 Integrate[f[x], {x,0,1}]] I think the output should ...
1
vote
1answer
113 views

Partial differentiation mixes up variables

Consider $$ U \equiv \dot{\theta} - \theta \ ,$$ where as per usual $\dot{\theta} = \frac {d \theta}{dt}$. We then have $$ \frac {\partial U}{\partial \theta} = -1 \quad , \quad \frac {\partial ...
0
votes
0answers
77 views

Fourier Transformation of a List

As we know the FourierTransform goes a function of t ,for example, f[t] to ...
1
vote
1answer
113 views

Complex Integration

There are some sequential functions: ...
6
votes
0answers
149 views

Suspected bug in Integrate

Bug introduced in 9.0.1 or earlier and persisting through 10.0.2 or later In version 10.0: ...
0
votes
1answer
69 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
2
votes
1answer
98 views

How to check if Integrate solved the integral?

This seems something that must have been asked before, but I am not able to find something. Integrate does not return status nor throw error when it can't find antiderivative. It just returns the ...