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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5
votes
1answer
101 views

Somewhat Irreproducible Integrate Results

Backslide introduced in v10 and persisting through v10.3.1. In the course of considering question 102922, I encountered erratic results from a particular integration. It is illustrated as follows. ...
5
votes
1answer
74 views

Behavior of D and Derivative when acting on functions with Rules as arguments

I was (pleasantly) surprised that when a Derivative is taken of a symbolic function for which the last few arguments are Rules, ...
2
votes
1answer
97 views

Limit $\sqrt{3-x}$ as $x\to3^+$ [closed]

I'm trying: $$\lim_{x\to3^+}\sqrt{3-x}$$ Using real numbers, technically this limit does not exist. However, Limit[f[x], x -> 3, Direction -> -1] I also ...
5
votes
2answers
153 views

Symbolic integration of SphericalBesselJ

Backslide introduced in v10 and persisting through v10.3.1. Consider the following integral ...
0
votes
1answer
93 views

Integrating the derivative of a function does not give expected result [closed]

I was trying to do the following integral: f[z_]:=Hypergeometric2F1[1,-a,1-a,1/(1-z)]/((1-z)^a-1) Integrate[D[f[z],z],z] I thought the result should be ...
8
votes
2answers
242 views

Can your Mathematica do the following integral?

Backslide introduced in v10 and persisting through v10.3.1. I was trying to do the following integral in Mathematica: ...
4
votes
0answers
105 views

Exploring formal limit definition

I found a few demonstrations on the Wolfram Demonstration Project site that help users to explore the formal definition of a limit. That is, $$\lim_{x\to a}f(x)=L$$ if and only if for every ...
8
votes
1answer
268 views

Strange bug: Product[1/(1-1/2^(n-1)),{n,2,Infinity}] = 0?

This infinite product is correct: Product[1/(1 - 1/2^n), {n, 1, Infinity}] (* 1/QPochhammer[1/2, 1/2] *) Numerical value of this result is not equal to zero ...
-1
votes
2answers
57 views

computing a limit [closed]

I couldn't compute this limit: it should be -3. I couldn't find the analytic way to compute it.
4
votes
1answer
103 views

Parametric numerical integration [closed]

I would like to solve the integral: $$ \iiint\frac{e^{-\sqrt{x^2 + k^2}}x^2 \sin{\theta}}{\sqrt{x^2 + k^2}} dx d\theta d\phi$$ defined in $x \in [0,+\infty]$, $\theta \in [0,\pi]$, $\phi \in [0,2 ...
3
votes
1answer
80 views

Newbie Problem with integral

when I type Integrate[Sign[x], x] to Mathematica, the answer is ∫Sign[x] dx so nothing new. When I type the same to Wolfram ...
1
vote
0answers
117 views

How do I calculate this integral along a complex line (not a contour) in mathematica?

Given the function: $$f(z) = \frac{\pi ^2 \cot(\pi \sqrt z) \cot(\pi \sqrt {z-a})}{4\sqrt{z^2 - az}}$$ Where a is a positive constant and: $$z = \frac{i}{b} + t $$ $$t>a$$ Where b is also a ...
3
votes
2answers
106 views

Correct behavior of Integrate involving logarithmic cut, or possible bug?

I just discovered that Integrate with simple poles in its integrand sometimes gives different results depending on number type of its limit (Exact vs Inexact). ...
0
votes
0answers
83 views

Mathematica: Derivative appears to be wrong

I'm first getting f(x) by computing an implicit equation. Then I want to take the derivative. Later on, when I plot both f(x) ...
3
votes
3answers
263 views

Computing the area between two curves

I want to find the area in between the two curves whenever they overlap each other. I've tried multiple different formulas but none of them have been working. I have to find it using the ...
10
votes
2answers
219 views

Demonstrating the behavior of a function as its independent variable approaches zero

I have several questions regarding the function $$f(x)=\frac{\sqrt{x^2+9}-3}{x^2}$$ that I would like to help my students with in the upcoming semester. Now, the limit as $x\to 0$ is 1/6. ...
5
votes
2answers
205 views

RegionPlot of ImplicitRegion is incorrect

Bug fixed in 10.4. Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect ...
2
votes
1answer
63 views

Using a grid table to estimate a limit

Consider finding the limit of $f(x)=(x^2-4)/(x-2)$ as $x\to 2$. f[x_] := (x^2 - 4)/(x - 2); I'm looking for some easy ways for my Calc I students (next semester) ...
0
votes
0answers
101 views

Error Message: Invalid integration variable or limit(s) in 1

I write the line: Integrate[1/{1 + Sin[2 x]}, x] And gives the error message: Invalid integration variable or limit(s) in 1. No solutions I'm trying work, and other integration problems are working ...
6
votes
3answers
812 views

Why does Mathematica spit this back out?

I'm struggling with the integral, $$\iint\sqrt{4a^2-x^2-y^2}dxdy$$ taken over the upper half disk of radius a centered at (a, 0). When I type it into Mathematica (10.2), Mathematica spits it back ...
1
vote
0answers
43 views

When evaluating this integral Mathematica returns two different answers

When evaluating this integral in Mathematica 10.3 Student Edition: ...
1
vote
1answer
100 views

Evaluate a double integral over a region [duplicate]

How can I evaluate a double integral over a region in Mathematica? For example $\qquad \iint(x^4+y^2)\,dx\,dy$ for the bounded region $y=x^2$ and $y=x^3$
9
votes
1answer
135 views

Non-rectilinear integration of InterpolatingFunction

Bug introduced in 7 or earlier and persisting through 10.3.1 [CASE:3487737] I have a 2-d array that I would like to resample into a different coordinate system and integrate along one of the new ...
1
vote
1answer
78 views

Integrating sinc function over discontinuity

I would like to analytically integrate the sinc function. First of all, if I just perform the integration the following way, everything is as expected: ...
2
votes
1answer
128 views

Triple/Double integral over outer side of a cylinder

$$\underset{S}{\iint} (yz\text{dx}\text{dy}+xy\text{dxdz}+xz\text{dydz})$$ Where S is the outer side of a part of a cylinder: $ x^2+y^2 = r^2 ; x\le0,\ y\ge0, \ 0\le z\le H$ The problem about that ...
2
votes
1answer
101 views

Two different results for same symbolic integral

I am trying to compute the following integral $\int_0^\infty dk \frac{e^{i k a}}{k^2}[\sin(kb)-kb\cos(kb)]$ When computing it as-is, i.e, with the code ...
2
votes
1answer
157 views

Why the strange limit?

When we take the limit, we get an Interval. Why? What does it say about the function? I know that when $0$ or $\pi$ are substituted we get exact values, otherwise ...
1
vote
1answer
99 views

How to show steps of Integrate[Exp[-(I*(s*t))]/(Sqrt[2*Pi]*Sqrt[s]), {s, 0, Infinity}]? [duplicate]

I am trying to use Wolfram Alpha in Mathematica 10.2 to show me the steps for calculating the integral in the title, i.e I have written the following command: show steps of ...
7
votes
1answer
74 views

When is RegionMeasure[ImplicitRegion[…]] faster than (N)Integrate[Boole[…]]?

I wanted to use Mathematica to compute areas and volumes of various implicitly defined regions, so I ran a simple test case using the unit circle: ...
3
votes
3answers
92 views

Integrate not restricting variable with Assumptions option?

I am integrating g over the region: ...
5
votes
3answers
119 views

Integrate is giving finite result for divergent integral

Integrate[Exp[c x]/x, {x, -a, a}] returns ...
0
votes
1answer
70 views

Integral Bounds and RegionPlot3D

We a tough problem in class today preparing for the final exam next Monday. $$\int_0^{\pi^{1/4}}\int_0^z\int_y^z 12y^2z^3\sin(x^4)\,dx\,dy\,dz$$ I was extremely surprised that I could simply type in ...
1
vote
1answer
122 views

Integrating differential solid angle over the unit hemisphere

When reading about rendering topics I commonly run into integrals over a hemisphere similar to this one: $\int_\Omega n \cdot l \, d\omega$ If I want to put that in Mathematica then I can ...
0
votes
1answer
98 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 ...
0
votes
2answers
58 views

Why i cannot get a numerical result? [closed]

I have tried following code: Limit[((sinx)^6)/(cosx - e^(-(x^(2))/2) + (x^(4))/12), x -> 0] Following is the image representing what I have tried to ...
0
votes
0answers
95 views

Integrate dealing with Sqrt gives wrong answers

I often find when I integrate something with a Sqrt[x] term in it, Mathematica gives an incorrect result. I assume this must be due to some kind of incorrect ...
2
votes
3answers
112 views

How to typeset and evaluate $u \big|_a^b$

Sometimes I need to evaluate an expression at the end points. e.g. the right hand side of $\int_a^bf(x)\textrm{d}x=F(x)\big|_a^b$. $F(x)$ could be complex at the right hand side so I can't just ...
0
votes
2answers
89 views

Using Mathematica to find the areas described by polar curves

I am working on a project and I need to find the area of the surface inside the polar-curve $r=2\cos(\theta)$ and outside the polar-curve $r=1$. The graph is pretty straightforward: just two ...
0
votes
1answer
37 views

Efficient calculation of leading order behavior of rational function under a limit?

Considering a rational function, as for example myExpr=(x+3)(2+5x+6x^2)/(x(x-5)(x+20)) I would like to have a function that tells me the leading order behavior ...
4
votes
2answers
147 views

Derivative of piecewise function

I tried to find $f'(0)$ of this function: $$f(x) = \begin{cases} x\cdot\sin(\frac{1}{x}) & \text{if $x\ne0$} \\ 0 & \text{if $x=0$} \end{cases}$$ This is what I tried in Mathematica: ...
3
votes
1answer
86 views

Evaluate Limit only if both directions(sides) are equal?Ex: $\lim _{x\to 0}\left(\frac{1}{x}\right)=DNE$

I want the limit of a function to only evaluate if both the left and right hand side are equal. For example $\lim _{x\to 0}\left(\frac{1}{x}\right)$ doesn't exist(two sided limit). However, the right ...
1
vote
1answer
169 views

Plotting singular integral

I need to plot the following singular double integration $u(x,t)$ for $t=0, t=0.2, t=0.4, t=1$ and $t=2$ in one figure as a line. That is, I need $u$-coordinate vertically and $x$-coordinate ...
2
votes
1answer
95 views

How to evaluate the limit of a function consists of Range

I would like to evaluate the limit: $$ \sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5+\cdots}}}}} $$ Therefore, I write the following function of n: ...
4
votes
2answers
87 views

Defining arbitary Derivatives of functions

If I have two functions like these f[a_,b_] and g[a_,b_]. Lets say ...
1
vote
1answer
46 views

Apply Grad and Mod to Matrix

Let f:=x^3+y*x*z+z^3; Let mat = {{2, 2, 2}, {3, 1, 7}, {1, 6, 3},{4, 5, 1},{0,4,9}}; be a list of points . I want to compute ...
2
votes
2answers
78 views

How to fix internal error “too much recursion” when trying to compute a definite integral

I'm completely new to Mathematica. I got a 14 day free trial and I'm using the online version. I'm trying to use it to check the results of an integration I performed by hand. But I'm not getting any ...
0
votes
2answers
104 views

How can I calculate the following integral?

I tried to calculate Integrate[(9.07 - 5.60 Cos[.87 t] - 2.71 I Sin[.87 t] + 2.14 Cos[1.74 t] + 2.70 I Sin[1.74 t] )^0.5, {t, 0, T}] but the output is the ...
1
vote
1answer
81 views

Evaluation of this definite integral

I want to obtain the symbollic expression for this integral: $\int^\infty_{-\infty} \, dx \, \left(\frac{y - x}{R^2 + (y-x)^2}\right)\, e^{-\frac{(x - \mu)^2}{4 s^2} - \frac{i k (y - x)^2}{2 R}}$, ...
5
votes
2answers
90 views

Infinite sum not evaluated unless split into even and odd terms

This sum s = Sum[Gamma[k/2]/(2 k!), {k, 1, ∞}] $\sum _{k=1}^{\infty } \frac{\Gamma \left(\frac{k}{2}\right)}{2 k!}$ is returned unevaluated (version 10.1.0). ...
0
votes
1answer
117 views

Calculate overlap coefficient between two functions

I have two functions and I want to calculate the overlap coefficients between those two functions. A similar question has been answered for Python and R, however, I couldn't find an answer for ...