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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10
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0answers
135 views

Strange behaviour of integrals with Cos, Sin, and Exp

During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would consider it a bug. ...
1
vote
2answers
104 views

Numerical integration does excessive coarse-graining?

I am trying to perform numerically the following integral $$\int_0^8\text{d}x\,\text{Re}\left[\frac{e^{-\frac{a^2}{2}-\frac{x^2}{2}} x^4 \sin (b x)\left(e^{-i c x} \text{erfc}\left(\frac{-c +i x ...
0
votes
2answers
82 views

Jump boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition ...
3
votes
1answer
44 views

Why does the following integral generate an error message for Delete::partw and Integrate`ImproperDump`tmp

The following integral generates a couple of errors that I'm not sure what they mean or how to prevent them ...
6
votes
1answer
142 views

Strange DiracDelta integration results in 10.4.1

Integrate[DiracDelta[s (x - c)] x, {x, -Infinity, Infinity}, Assumptions -> {s > 0, c > 0}] gives me c/s in ...
1
vote
0answers
236 views

A power series expansion [closed]

Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
0
votes
2answers
131 views

The Disc and Washer Methods [closed]

How is it possible to demonstrate a visual solid of revolution utilizing the washer method? For example to show the shape formed by rotating the region bounded by $y=(x-2)^4, 8x-y=16$ about $x=10$? ...
1
vote
1answer
68 views

Inconsistent Integrate behavior?

Evaluating the following integral with Mathematica Integrate[q0/(-1 + q0^2), {q0, 0, A}] gives a conditional expression ...
0
votes
0answers
38 views

Construct certain univariate functions over bounded interval having given set of moments [migrated]

We have a class of probability distributions (parameterized by $\alpha =\frac{1}{2},1,\frac{3}{2},2,\ldots$) over the interval $[-2^{-12} \cdot 3^{-3},2^{-16}]$ having as their $n$-th moments ...
0
votes
1answer
359 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
5
votes
1answer
75 views

ComplexInfinity for a convergent product

The infinite product involving the ratio of (n^2)! to its Stirling approximation ...
0
votes
0answers
32 views

Inverse Fourier Transform [migrated]

I have to calculate the following Inverse Fourier-Transform, which describe the potential function for a point force on a half-space: ...
3
votes
2answers
95 views

Are there any code which just derivative of piecewise function(same distence)?

I wrote this code: Piecewise[{{x^2, 0 <= x <= 1}, {x, x <= 4}}] and I got derivative of this code: ...
10
votes
1answer
141 views

Teaching Mathematica more about DiracDelta and KroneckerDelta

As the documentation and some experimentation indicates, Mathematica contains little information about representations of the DiracDelta and ...
1
vote
2answers
50 views

Integration over variables

I'm trying to take the integration of 1/x over v0 and vt. I want it to output: Ln(v0 / vt) or at least Ln(v0) - Ln(vt). I tried ...
0
votes
0answers
31 views
1
vote
2answers
156 views

Why can't Mathematica integrate this PDF?

I'm trying to integrate a transformed Gumbel PDF in Mathematica. Integrate[E^(η*(-(x - q)) - E^((-η)*(x - q))), {x, t, ∞}] However, it doesn't compute. It's fine ...
0
votes
2answers
278 views

Why the result by hand is different from the built-in DSolve?

Yesterday, I used Mathematica to solve a differential equation using the built-in command DSolve[]: ...
0
votes
2answers
94 views

Numerical derivative from data points

I want to take the second derivative of a set of data points (at the point $x = 0$). Let's assume that this set looks like that ...
2
votes
1answer
101 views

Maximize a variable in NSolve Function

I want to solve a set of trigometric coupled equations with the NSolve funcion while at the same time trying to maximize a variable which has to be real and between ...
3
votes
1answer
53 views

Dirac delta in integrals

I am trying to simplify the following integral ...
5
votes
2answers
143 views

Derivatives of piecewise functions of functions

Background Derivatives of piecewise functions in Mathematica are computed according to special rules. According the Piecewise documentation (see Possible Issues), ...
0
votes
1answer
56 views

Partial derivative of function of two variables

This question is not enlightening nor is it difficult. But some part of my notation or how I have defined my functions is messing up the D[f,x] function. ...
0
votes
1answer
104 views

Elliptic integral of the first kind [closed]

I want to plot the integral $$I(\phi) = \int_0^{\phi} \frac{\mathrm{d} \theta}{\sqrt{1 +\sin(\theta)^2}}$$ In Mathematica notation, it is a case of an elliptic integral of the first kind with $m=-1$, ...
5
votes
4answers
243 views

Results in terms of a function

Let's assume I have a function $f(x)=\exp(10x^2)$, i.e. f[x_]:= Exp[10*x^2]. When I differentiate $f$ by evaluating the expression ...
7
votes
2answers
162 views

Sets and sums of different elements

Consider the set S={w,x,y,z}. If the set of all possible sums of any three different elements from S is {-1,3,5,8}, then what is the set S? How could I solve this function using Mathematica?
1
vote
1answer
37 views

How to specify assumptions without typing out functions

So I want to add assumptions in carrying out integration. I know I could use the Integrate function: Integrate[V Exp[-x/a] ,{x,0,10}, Assumptions->a>0] but ...
0
votes
1answer
142 views

Solving integral

How can I solve this integral: Integrate[expression, x] where expression is: ...
2
votes
2answers
116 views

Any reason why this definite integral is so slow to compute and the indefinite fast?

This integral is easy and fast to compute Integrate[Sqrt[(x^2) + k ], x] $$\frac{1}{2} x \sqrt{k+x^2}+\frac{1}{2} k \log \left(\sqrt{k+x^2}+x\right)$$ But ...
10
votes
1answer
449 views

Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
5
votes
2answers
236 views

Orthogonalize polynomials with respect to Gagliardo seminorm?

For a function $f\colon [-1,1]\to\mathbb{R}$, the Gagliardo seminorm of $f$ is defined to be $$ |f| = \int_{-1}^1\int_{-1}^1 \frac{(f(x)-f(y))^2}{(x-y)^2}\, \mathrm{d}x\, \mathrm{d} y. $$ Given ...
1
vote
1answer
60 views

How to find the pole of a equation where the residue exist?

I want to calculate the residue of an equation, such as: equ = 1/((x - 2)Sqrt[x - 1]) So first I need to find the pole of the equation. My method is find the ...
8
votes
1answer
205 views

Strange result of parameter-dependent definite integral

Inspired by this question on Math.SE, I wanted to see what Mathematica could do with the integral $$ \int_0^{\pi}e^{k\cos t}\cos(k\sin t)\,dt. $$ Thus, I entered into Mathematica (tried on both 10.3 ...
0
votes
1answer
100 views

Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
2
votes
2answers
447 views

How to find the area between 3 curves?

I have three equations: $y=3/x$, $y=12x$, and $y=x/12$, $x>0$. I am not sure how to go about integrating an equation once I find the intersections. Do I need multiple integrals?
6
votes
1answer
110 views

Animate the line integral over a scalar field

There is a gif from Wikipedia, The line integral over a scalar field $f$. How to plot and animate this in Mathematica?
0
votes
1answer
86 views

Integral not giving expected answer [closed]

Below is the integral I'm trying to evaluate: ...
4
votes
2answers
163 views

How does Mathematica calculate integrals? [duplicate]

One can use mathematica to get $$ \int_{-\infty}^{\infty}\frac{\sin^2x}{x^2+1}\ dx=\frac{\pi \sinh 1}{e}. $$ Here are my questions: [Edited:] Is there a way that I can see the intermediate steps ...
5
votes
1answer
397 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
5
votes
2answers
180 views

Definite integral closed-form expression

Is there a way to get Mathematica yield a closed-form expression (in terms of special functions) for the integral: $$ \int_{0}^{\infty} e^{-a t}\log(t)\log(1+t)\,dt, $$ where $a>0$? The obvious ...
1
vote
2answers
118 views

How to find the limit of a function of two variables

I was wondering if there is a method to find the limit of a function of two variables at a point. I tried the following: ...
-2
votes
1answer
89 views

How would I find the area of a function over a specific interval? [closed]

How would I find the area of a function over a specific interval? For example: $g(x) = e^{5x}$ Find the area of the function over the interval $[-4, 2]$.
1
vote
1answer
165 views

How I can get faster code for computing a fractional integral?

I use of this code Fractional Integral and wrote the following code: ...
1
vote
0answers
61 views

Limit not evaluated [closed]

I hope this question ha not been asked since the limit is evaluated in 1 not at 0 or infinity. I do not know how to ask Mathematica to find the limit as n -> 1 of the following function: ...
0
votes
1answer
76 views

Rotate from 0<=X<infinity [closed]

Find the volume of the solid obtained by rotating the region below the graph of y = e^(−x) about the x-axis for 0 ≤ x < ∞ With that given expression I tried to do it by doing the following code: ...
6
votes
2answers
176 views

Probability of distance of two random points in the unit circle

Inspired by the problem solve this probability problem symbolically which I have already generalized there I'd like to ask here the same question for a unit circle. More precisely: given two randomly ...
0
votes
0answers
53 views

Sum of Infinite convergent series

I have a series as Sum[(x^1 - (x - 1)^1) (b^Log[(1 + (x))]), {x, 1, Infinity}] which is convergent when b=0.3 and ...
0
votes
0answers
22 views

Syntax Error with Expectation over Distribution

I am getting some errors when I try to execute the following code. Here, the expectation is taken over $g$ which has Nakagami Distribution. ...