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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0answers
43 views

When evaluating this integral Mathematica returns two different answers

When evaluating this integral in Mathematica 10.3 Student Edition: ...
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1answer
106 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
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1answer
137 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 ...
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1answer
84 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
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1answer
130 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
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1answer
107 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
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1answer
158 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
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1answer
109 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
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1answer
75 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
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3answers
93 views

Integrate not restricting variable with Assumptions option?

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

Integrate is giving finite result for divergent integral

Integrate[Exp[c x]/x, {x, -a, a}] returns ...
0
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1answer
71 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 ...
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1answer
129 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
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1answer
102 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
59 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
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3answers
113 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
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2answers
97 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
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1answer
39 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
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2answers
157 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
91 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
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1answer
171 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
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1answer
100 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
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2answers
89 views

Defining arbitary Derivatives of functions

If I have two functions like these f[a_,b_] and g[a_,b_]. Lets say ...
1
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1answer
47 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
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2answers
82 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 ...
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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
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1answer
85 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
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1answer
139 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 ...
2
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3answers
118 views

Adding more specific assumptions to Integrate

Let's say I would like to find a symbolic form for the integral $$\int_0^{2\pi}\sin^nx\,\mathrm{d}x$$with the added condition that $n$ is not only an integer, but an even one at that. Can this be ...
2
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0answers
90 views

How to Mellin transform a complicated Log integrand?

I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this: $$ \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
2
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0answers
65 views

Good coding for integral substituions

This question is aimed at improving both my coding and my understanding of MMa's capabilities. A lot of my code is still hacks and workarounds for things I don't know how to do properly. I want to ...
4
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1answer
105 views

Mathematica shuts down when calculating this limit

Bug introduced in 9.0.0 and fixed in 9.0.1 I'm trying to compute this limit: Limit[E^-(r^2)^(2*n)*r*2*Pi, n -> Infinity] But, when I run the code above, ...
19
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2answers
317 views

Derivative of a pure function with SlotSequence

I can live with this but I can't figure out why the following is 0: Derivative[1][f[##] &][x] 0 From documentation ...
16
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1answer
266 views

Integrate returns imaginary answer for smooth, real function

Bug introduced in 7 or earlier and persisting through 10.4 I'm trying to evaluate the integral: $$\int_0^{\infty} \frac{1}{4 b \sqrt{\pi} r} e^{-(b-r)^2}(e^{4 b r} - 1) \mathrm{d}r$$ with ...
2
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1answer
96 views

Problem with imaginary/real parts of a complex function

I have a problem with this code: ...
0
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1answer
118 views

Reflective and Constant Flux Boundary Conditions

Can anyone tell me how I can use NDSolveValue to model reflective and constant heat flux boundary conditions. I am solving the heat equation. Essentially I have a ...
0
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0answers
38 views

Possibility of an output for this integral

Any clues as to whether an output exists for this expression where t and f are positive real numbers that can be treated as constants ...
3
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1answer
70 views

Numerical integration with parameter and plot

I'm working on this function: (0.0027 Sin[phi])/(1.05*Exp[-241w]+ Exp[239w]-Cos[phi]) I'd want NIntegrate this function on ...
1
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1answer
54 views

Integrating the product of two imaginary error functions

I am trying to evaluate the following integral: Integrate[Erfi[y] Erfi[z + y] , {y, -L, L}] which simply returns the input. How could I force ...
0
votes
1answer
65 views

Getting numerical values from integrated interpolating function [duplicate]

I have a list of data. I integrate them with interpolation. Lets say is the following: InterpolatingFunction[{{0.01, 4.82}}, <>][x] However, is that ...
2
votes
1answer
74 views

Define a function that is an integral that takes a function as argument [closed]

How can I define a function $F$ in Mathematica that does the following: $$F(a,b,P) = \int_a^b P(1-t) \, dt,$$ where $P(t)$ is some function, say, a polynomial? More specifically, I would like to be ...
1
vote
0answers
53 views

Mathematica refuses to integrate a function it knows how to integrate [closed]

Let $a$, $b$, and $k$ be positive real numbers, and consider the integral $$ \iiint\limits_{\mathbf{x} \in \mathbb{R}^3} \delta(a \lVert \mathbf{x} \rVert^k -b) \ \mathrm{d}^3\mathbf{x} = ...
4
votes
1answer
117 views

Integration of a piecewise function

Define f[x_, i_] := Piecewise[{{1/n, 0 < x < (i - 1)/n}, {(i/n - x), (i - 1)/n < x < i/n} , {0, i/n < x}} ]; I would like to compute ...
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1answer
173 views

Dealing with indicator functions

I am calculating the integral of two indicator functions with Mathematica. I'm having difficulty in imposing assumptions. What I have done so far: To define an indicator function: ...
7
votes
3answers
1k views

Region bounded by x^2+y^2=1, y=z, x=0, z=0, in first octant

I need to draw (pencil and paper) the region bounded by $x^2+y^2=1$, $y=z$, $x=0$, and $z=0$ in the first octant. So the first assistance I asked of Mathematica is: ...
2
votes
1answer
108 views

How to solve this definite integral in mathematica?

I am a beginner in mathematica. I tried to solve this integration but not able to solve it. Can any body help me how to solve this integral in mathematica? Here is my integral, $$\int_{a}^{b} ...
0
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0answers
64 views

To calculate the differential of a function

I need to calculate the differential of a function WaveNumber. However, when I compile the code, it generates followig error: Infinite expression 1/0. ...
2
votes
1answer
218 views

Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...