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)

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: ...
5
votes
2answers
137 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), ...
1
vote
0answers
60 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: ...
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: ...
0
votes
0answers
49 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. ...
-1
votes
1answer
90 views

Double integrals in quantum chemistry [closed]

In quantum chemistry we often encounter integrals like this: I can't understand what is the problem. Can anybody help me?
0
votes
1answer
64 views

Why does Mathematica 10.3.1 fail me on : Integrate[(x^3) [Log[2 Sin[x]]]^8, {x, 0, Pi}] [closed]

All it gives me is a pretty restatement of my original request. When I use WolframAlpha PRO, I get a result of 624510 and a visual representation of the area in question. I know the ends of the ...
6
votes
2answers
172 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 ...
3
votes
1answer
106 views

Calling Integrate with many limits of integration

I accidentally discovered that you can put many numbers into the limits of integration of Integrate and Mathematica will still evaluate it without returning an ...
10
votes
0answers
131 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. ...
4
votes
3answers
186 views

How to solve this integration? [closed]

I need to find the integration of the following expression ...
1
vote
2answers
91 views

Asymptotic form of the “strange” function

I want to find the asymptotic form of this function ...
0
votes
2answers
90 views
4
votes
1answer
86 views

Am I getting a correct answer with the Dt command?

We are asked to find $dy/dx$ when $x^y=y^x$. Our hand calculations use logarithmic differentiation. $$\begin{align*} x^y&=y^x\\ \ln x^y&=\ln y^x\\ y\ln x&=x\ln y\\ \end{align*}$$ Then we ...
2
votes
3answers
90 views

How to find nth log derivative using mathematica?

Now I have a function, say $f(k,z)=e^{-kz}(1+kz)$ I want to find the $n$th $\log$ derivative with respect to z. like $(z\partial_z)^{(n)}f(k,z)$ (or $(\partial_{\ln z})^{(n)}f(k,z)$ if you like), ...
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 ...
13
votes
5answers
510 views

solve this probability problem symbolically

Consider a unit square, Pick two points P and Q uniformly at random inside the square, What is the probability that |PQ|>1? I tried solve this problem ...
7
votes
4answers
470 views

How to find a tangent line with 2 points of tangency for a curve?

Say I have a function like this: f[x_] := 4 x^4 - 9 x^3 - x^2 + 10; Plot[f[x], {x, -1, 2}] It's obvious that there's a tangent line with 2 points of tangency ...
0
votes
0answers
24 views

Jackson integral applied to a recursion

Two days ago I asked a question about the way to compute a Jackson integral $\int_0^t h(x[s]) d_qs$. But now, I must applied it in the follwing recursion : $ \left\{\begin{array}{l} x_0[t,q] = ...
0
votes
1answer
43 views

Dependency of parameter to find maximum vanishes after simplification

EDIT: It turns out I just made a dumb mistake: Simplify[Exp[x^2]*2^n*Pi*D[maxdist[n,x]/n*(1+Erf[x/Sqrt[2]])^(2-n),x]] A portion of my "factor" is actually inside ...
3
votes
1answer
88 views

Writing a function that finds the difference between two maxima

Suppose i have two functions: $\qquad -2x^2 +5x+3$ and $\qquad -5x^2 +2x+3$ To solve the point where the functions are at maximum i use the command NMaximize ...
3
votes
1answer
109 views

Jackson Integral

Following an old post, I have tried to make a function that calculates the Jackson integral of $q$-calculus: ...
0
votes
0answers
55 views

Integrate an expression and simplify the result

I have to find the indefinite integral of the following: $$\int\sqrt{ax^4 + bx^3 + cx^2 + dx + e} dx$$ where a, b, c, d, e are constant of the order 0.0001 or less but always greater than 0. I ...
1
vote
1answer
54 views

Total and partial derivatives [closed]

The following piece of Mathematica code calculates the total derivative of a function $f(x,y(x))$ and compares it with what it should be. However, the result is not zero: ...
10
votes
1answer
136 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
97 views

How to convolve the unit box function and the modified Bessel function of the second kind in 2D?

In 1D the convolution of the unit box function and the modified Bessel function of the second kind $K_0(x)$ works very well. ...
0
votes
0answers
62 views

Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
1
vote
3answers
56 views

A function calculating a multiple integral and taking multiplicity as a parameter

I have a function of the following form: $$ \varphi_n(x)= ...
3
votes
1answer
52 views

Integrating a gradient and matching terms automatically

I am trying to integrate a function $\nabla w(x,y)$ indefinitely knowing both components of $\nabla w(x,y)$. I have a function dw[x_,y_] that I have defined. I then ...
0
votes
0answers
76 views

Setting up and solving an equation

I would like to solve the equations: $$ F(\xi;x,t)=\int_0^\xi u_{0}(\xi)\:d\xi+\frac{(x-\xi)^{2}}{2t} $$ to use in evaluating: $$ u(x,t)=\dfrac{\int_{-\infty}^\infty \dfrac{x-\xi}{t} ...
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 ...
2
votes
2answers
114 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 ...
0
votes
0answers
33 views

How can I get left-sided-sequence with InverseZTransform

InverseZTransform[z^2/((4 - z)*(z - 1/4)), z, n, Assumptions -> {1/4 < Abs[z] < 4}] (* -(1/15) 4^-n (-1 + 16^(1 + n)) *) the result is not true.It only ...
1
vote
1answer
118 views

Summing infinite series that converge only for some parameter values

The input Sum[d^t,{t,0,Infinity}] produces output 1/(1-d) which is correct for $|d|<1$. But for $|d|\geq1$ the sum does ...
1
vote
1answer
31 views

Mathematica Integral[] return [closed]

I am new to mathematica and while trying to find the double integral of 8-xy over -2 ...
1
vote
2answers
135 views

How to do this integral? [closed]

Is there any workaround to do this integral? Integrate[(x^2+2 x+1+(3 x+1) Sqrt[x+Log[x]])/(x Sqrt[x+Log[x]] (x+Sqrt[x+Log[x]])),x]
0
votes
0answers
108 views

Implicit hidden assumptions of Mathematica with Limit

I've stumbled upon the following symbolic limit (a tricky one): Limit[(Sqrt[2] v)/Sqrt[v^2 - c^2 (1 - 1/c Sqrt[c^2 - v^2])], v -> 0] Mathematica gives 0 as ...
8
votes
0answers
84 views

Slot number cannot be filled

I got a strange message with the derivative of a two-argument function defined by a definite integral. For example if "f" is defined as: ...
2
votes
1answer
81 views

Getting wrong result when Integrating under an assumption [duplicate]

The simple integral $$\int_0^b \cos\left(\frac{2\pi m(y-\eta)}{b}\right) \cos\left(\frac{2\pi \eta}{b}\right)\mathrm{d}\eta$$ can be easily evaluated by Mathematica as, ...
0
votes
0answers
51 views

Using DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
0
votes
0answers
40 views

Problem with indefinite integral

How do I calculate this integral with mathmatica? integrate[(Exp[-x/a]Exp[-p x/a])/(x^2 (1-(a/t)^2 Exp[-2 x/a])^(1/2)),x] a, p, t are constants
-2
votes
1answer
55 views

Finding unit vectors which makes an angle 60 degrees with both {1, -1, 0} and {1, 0, -1} [closed]

Find unit vectors which makes an angle 60 degrees with both vectors {1, -1, 0} and {1, 0, -1}.
3
votes
1answer
92 views

Indefinite integral of nested trig functions [closed]

I tried vainly to integrate nested trig functions like Integrate[Sin[Cos[x]], x] Mathematica does not find a solution. At first I thought there was no solution, ...
6
votes
1answer
88 views

How correctly use WhenEvent to detect when gradient is over a certain value?

So I wish to stop integrating my PDE when the spatial gradient is larger than some value, let's say 10. That is to say, my WhenEvent condition wants to be stop when the the maximum gradient over all x ...
0
votes
1answer
53 views

Evaluate as much of an integral as possible [closed]

Consider the integrand $\qquad \cos(x+\sin^{-1}(x)) = \sqrt{1-x^2} \cos(x) - x \sin(x)$ If I ask Mathematica to integrate $\cos(x+\sin^{-1}(x))$, Mathematica is unable to do so analytically (due to ...
4
votes
3answers
231 views

How can I plot a paraboloid?

How do I plot a function for a paraboloid? Im putting together surfaces to model lipstick. I need the paraboloid for the top part and then I'll be cutting the paraboloid at angle with another surface. ...
3
votes
1answer
57 views

Evaluating function

I'm trying to evaluate this function, which is gradient of integral with variable limit of integration: $$ u(x,y,t)=\nabla(\int_{v(x,y)}^\infty \frac{e^{-b(t-\tau-c)^2}}{\sqrt{\tau^2-{v(x,y)}^2}} ...
1
vote
1answer
47 views

Unexpected behavior in symbolic integration with GenerateConditions->False

Consider the following two symbolic integrations: ...