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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2
votes
2answers
449 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
122 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
51 views

Error in partial derivative and replace?

After run my code, output is ...
0
votes
1answer
86 views

Integral not giving expected answer [closed]

Below is the integral I'm trying to evaluate: ...
4
votes
2answers
169 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 ...
-2
votes
1answer
91 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 $[-4, 2]$.
5
votes
2answers
191 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
119 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
151 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
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
78 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
167 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
60 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
23 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
96 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
68 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
182 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
109 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
141 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
193 views

How to solve this integration? [closed]

I need to find the integration of the following expression $$H(k)=\frac{\tau_0}{\pi}\int_0^{\infty}\exp\left(-u^{\delta}\cos\left(\frac{\delta\pi}{2}\right)\right)\cos\left(u^{\delta}\sin\left(\frac{\...
1
vote
2answers
94 views

Asymptotic form of the “strange” function

I want to find the asymptotic form of this function ...
0
votes
2answers
94 views
4
votes
1answer
89 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
100 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
209 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
514 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
480 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
26 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] = f[t]\\...
0
votes
1answer
45 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 ...
4
votes
1answer
91 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 ...
4
votes
1answer
120 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
57 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
56 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
147 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
132 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
64 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
59 views

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

I have a function of the following form: $$ \varphi_n(x)= \underbrace{\int\limits_\mathbb{R}\ldots\int\limits_\mathbb{R}}_{n}\exp\left[-\sum\limits_{j=2}^{n}\left(x_{j}-x_{j-1}\right)^2-(x-x_{n})^2\...
3
votes
1answer
57 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
77 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} e^{-1/2ReF}d\xi}...
1
vote
1answer
64 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
118 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
119 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
32 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
137 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
161 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 ...
10
votes
1answer
103 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
82 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
53 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
44 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