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

learn more… | top users | synonyms (3)

3
votes
2answers
136 views

Symbolic Integrate fails after almost 1 hr calculation

Mathematica 9. I want this Integrate[( Cos[t ω]^2 Cos[α + t ω])/(-1 + A Cos[α + t ω])^2, {t, 0, (2 π)/ω}] Can Mathematica handle with it? I tied different ...
2
votes
1answer
135 views

Residue failed to reproduce this residue in a paper

This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ...
0
votes
1answer
59 views

Integral of $(\sin x)^3(\cos x)^3$ [closed]

For the integral of (sin x)^3(cos x)^3 I got 1/6(cos x)^6 - 1/4(cos x)^4 + C. This seemed to work but my book had 1/4(sin x)^4 - 1/6(sin x)^6 + C. This is similar to what I got but instead of cosine ...
2
votes
0answers
62 views

Why does Expectation function compute, while explicit integration does not?

The code: Expectation[1 + 1/y, {y \[Distributed] ExponentialDistribution[1]}] outputs 1 - EulerGamma While, ...
2
votes
3answers
130 views

NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
1
vote
1answer
66 views

Problem in limit of exponential function

I want to obtain Exp[-α/(1 - α)] /. {α -> 1} The output is Indeterminate. But I calculate without Mathematica and I ...
1
vote
1answer
64 views

Need help on simplifying the integral of a square root of a polynomial

I have the following expression a = 4 Cos[af / 2]^2; b = 1 - 5 Cos[af / 2]^2; c = Cos[af / 2]^2; s = Sqrt[a*x^4 + b*x^2 + c] and I need the integration of $s$ in ...
3
votes
1answer
101 views

Using Vector Operations In Mathematica

I would like to calculate $$ \mathbf T = (\mathbf B \bullet \nabla) \mathbf B$$ Where nabla (the upside down triangle) is the grad operator $(\partial/\partial x,\partial/\partial y,\partial/\...
1
vote
1answer
105 views

Evaluate an integral with parameters

I already asked this on stack overflow but was redirected here. I am trying to solve the (highly non-linear) following system of equations : with and $g_0$, $\Lambda$ are positive constants ...
0
votes
2answers
183 views

Integrating SquareWave - don't understand result

Integrate[SquareWave[t], t] // InputForm Gives as output Piecewise[{{-t, Inequality[1/2, LessEqual, Mod[t, 1], Less, 1]}}, t] ...
3
votes
2answers
141 views

Integrate on a contour in the complex plane

I want to integrate the function f[z]= z + Conjugate[z] over a circle of radius 2 centered at the origin. For the sake of stating something that I have tried: <...
3
votes
2answers
92 views

Application of # for the $n^{th}$ derivative

Let's say that I have x^2+x Is there a way to map $x$ to the first derivative of a function and $x^2$ to the second derivative of the same function? According to ...
0
votes
2answers
96 views

How to set a line coordinate for a symbolic line integral over a curve? [closed]

I have the following closed curve, defined by a set of points. ...
1
vote
0answers
64 views

How to do this integral of Hypergeometric functions in Mathematica?

I've tried to integrate by part, but it seems that Mathematica is still not able to integrate. ...
4
votes
2answers
310 views

Double integral

The question is Calculate the double integral where D is an area enclosed by the following lines, ,, and I have tried doing it the following way but its wrong and I cant seem to get it ...
3
votes
1answer
268 views

Plotting the 3D region that determines a volume

I need to plot this with Mathematica: Use a triple integral to determine the volume of the region below $z = 4 - x\,y$ and above the region in the xy-plane defined by $0 \leq x \leq2,\ 0 \leq y \...
8
votes
1answer
141 views

Symbolic and numeric limit disagreeing on branch cut of ArcTan

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. Investigating comments to my previous question lead me to the following problem: ...
8
votes
2answers
158 views

Integrate and NIntegrate disagreeing over branch cut of Sqrt?

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. In Mathematica 10.2 I'm trying to integrate this piecewise continuous function, but ...
1
vote
1answer
52 views

nonatomic expression expected when trying to sum of the integrals of two functions

newbie to MMA. After computing the following two integrals: ...
0
votes
2answers
54 views

Issue while trying to compute the integral for the coefficients of a triangular wave

I was trying to compute these integrals in order to check if I was correct: or in code ...
2
votes
0answers
59 views

What does Mod^(1,0) mean in mathematica output [closed]

I am trying to take he derivative of mod(remainder). In:= D[Mod[x, y], x] Out = Mod^(1,0)[x,y] I cannot understand the meaning of Mod^(1,0). What does the ...
0
votes
2answers
103 views

Integral over real valued function becomes complex

I've tried to solve the following integral, but I get a complex solution even tough it should only have a real part. $$f(x)=- \frac{10^{-20} x}{0.99005- e^{10^{-12}x}}$$ Now I want to calculate the ...
1
vote
1answer
68 views

How to integrate with integer parameter in Mathematica?

I would like to integrate the following expression with N being Integer ...
9
votes
1answer
165 views

Wrong limit: Limit[(1 + (-1)^n/n)^n, n -> Infinity]=1 (Mathematica 10.4 and W-Alpha)

Since $(1-\frac{1}{n})^n\to 1/e$ and $(1+1/n)^n\to e$, the sequence $(1+\frac{(-1)^n}{n})^n$ has no limit as $n\to\infty$, but has limits for odds and even numbers. If $n$ were taken to be real, there ...
10
votes
1answer
251 views

Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions

Bug introduced in 7.0 or earlier and persisting through 10.4.1 This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore J....
0
votes
0answers
74 views

Tricky inverse Laplace transform

I'm trying to compute the inverse Laplace transform of $f(s) = s^c/(N + s^{ir} )$ where $c,N \in \mathbb{C}$ and $r \in \mathbb{R}^+$ using the Bromwich integral $$ F(t) = \frac{1}{2 \pi i} \int_{- ...
0
votes
1answer
87 views

Definite and indefinite integral give different results

I'm trying to find an expression that, given $x$, $y$, and $R$, gives the indefinite 2D integral of a function at the circle centered on $(x_0, y_0)$ with radius $R$. With $g$ as defined below, I'd ...
2
votes
1answer
84 views

Why does NDSolve and NIntegrate not give the same result? [closed]

I have plotted solution of two equivalent equations one in Integral form (right chart) the other in Differential form (left chart) using NDSolve and NIntegrate but they give me completely different ...
5
votes
2answers
262 views

Strange phenomenon occurring in analytic integration result involving Bessel functions

For the following integral, Integrate[x^2 Exp[-a x^2 - b x^4], {x, -∞, ∞}, Assumptions -> {a > 0, b > 0}] Mathematica gives the following analytic ...
1
vote
1answer
88 views
0
votes
0answers
42 views

Replace higher order derivatives given lower order derivative

I have an unknown function f[x1,x2] whose partial with respect to x1 is identically zero. I would like to make sure that ...
1
vote
1answer
63 views

Defining functions as derivatives

I'm working on a model that requires a sum over a function that uses various coefficients. In order to make the sum easier to perform, I am trying to keep things general through the use of a ...
3
votes
2answers
108 views

Problems with integrating over a region

Following the example of this answer: Find the volume of the region defined by $|x|+|y|+|z|<4$ I tried to compute the following integral over a region by using ImplicitRegion. However, when I ...
10
votes
1answer
1k views

How does a Pringle lose its curvature?

Nom! As part of a bigger project, I've was writing some code to calculate the scalar curvature of surfaces of the form $z = f(x,y)$. This uses a general calculation of the scalar curvature to produce ...
0
votes
1answer
86 views

Tedious integral

I'm new to Mathematica so I'm not familiar with its potential use to solve tedious symbolically integrals. I'm trying to solve the following one: ...
0
votes
1answer
62 views

integral involving square of exponential integral

I'm trying to compute the integral $$ \int_{a}^{\infty}\frac{e^x}{x}[\mathrm{Ei}(-x)]^2\,dx, $$ where $\mathrm{Ei}$ is the exponential integral, and $a>0$. The obvious ...
1
vote
0answers
17 views

Module command and differential equation [duplicate]

I write a programma see below ...
1
vote
1answer
123 views

From which version Mathematica will be available Symbolic n-th derivative? [duplicate]

On www.wolframalfa.com Symbolic n-th derivative works.
0
votes
1answer
44 views

Assumptions with Multiple Rules

What is the correct way to add more than one assumption while integrating? I am attempting to evaluate the following integral and Mathematica is just stalling, so I'm wondering if my assumptions are ...
2
votes
1answer
93 views

Dog chases his tail ! - “parametric differential/Integral equation”..?

I have the following situation where I am interested in the function $m(t)$ $$ \frac{dm}{dt}=4T(t)^{3}+T(t)^{2} $$ $$ T(\tau)=T_{0}-\int_{0}^{\tau}(\frac{dm}{dt})dt*Q_{S} $$ Is there a way to solve ...
2
votes
1answer
149 views

How to linearize an expression involving derivatives?

I want to linearize the expression involving function $y(x,t)$ $$[y^3(y_x-y_{xxx})]_x$$ by assuming $y(x,t)=y_0(t)+y\prime(x,t)$, where $y\prime(x,t)$ is a small variation. In other words, I will ...
6
votes
3answers
418 views

Integrate to calculate enclosed area

I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve': The curve is: $r=\sin 2\theta$, $\theta \in [0, \pi]$ which I believe is already in polar form. I ...
1
vote
2answers
235 views

How to compute this integral?

I'm trying to calculate this integral : $$I(z,k,a)= \displaystyle\int_{1}^{\infty} t^2\, \text{ArcTanh} \left(\sqrt{\frac{t^2-1}{t^2}} \dfrac{k}{z}\right)\, e^{-a\,t} \, dt$$ Where : $\textrm{...
3
votes
2answers
118 views

How to plot a volume for triple enclosed by surfaces

My main issue (multivariate calculus), I want to plot the body made within the surfaces y + z = 4, y = 4 - x^2, ...
2
votes
3answers
212 views

Mathematica Integration Problem

I am new user of Mathematica. Can anybody help me to solve this integration? I really needs your help. Integrate[(1 - (1/(1 + A x^(-ao)))) x, {x, 0, r}] Can not ...
3
votes
2answers
86 views

Integral invoving product of Whittaker functions

I'm trying to evaluate the integral $$ \int W_{0,a}(x)\,W_{1,b}(x)\,\frac{dx}{x}, $$ where $W$ denotes the Whittaker $W$ function, and $a,b\in[0,1/2]$. Using the Whittaker differential equations that $...
0
votes
1answer
44 views

I would like to be able to get this integral evaluation to show up in terms of variables

this is very much a beginner question; I was hoping that someone may be able to take a look at this code and tell me why it outputs all of these crazy numbers instead of just the variables specified ...
2
votes
0answers
66 views

Cauchy Principal Value

Cauchy principal value of the following integration gives nothing in Mathematica. $\int\limits_{-\infty}^\infty\frac{\text{dx}}{x-2}$ I tried some hand calculation which is $\lim\limits_{\...
-1
votes
1answer
38 views

Maclaurin Series Help [closed]

My problem is to numerically approximate the series (1 - Cos[x])/x over the interval [0,1]. I typed it into Mathematica as so: ...
0
votes
1answer
72 views

Faster code for calculat in Integral include derivative

I saw this question How I can get faster I tried help that. But I can not understand. I want to write a faster code for: ...