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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3
votes
2answers
96 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: ...
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

Using assumptions with Integrate [duplicate]

I open Mathematica and execute this code: ...
0
votes
2answers
95 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 ...
3
votes
1answer
53 views

Dirac delta in integrals

I am trying to simplify the following integral ...
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. ...
1
vote
2answers
157 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 ...
1
vote
3answers
109 views

How to calculate the double integral of a double integral?

May I ask is there any wise way to calculate the following integration? $\int_{-1}^{1}\int_{-1}^{1}\int_{-1}^{1}\int_{-1}^{1}\frac{\left( 0.25 \left(-1+\eta _1\right) \eta _1 \left(-1+2 \eta ...
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 $m=-1$, ...
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 ...
7
votes
2answers
163 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: ...
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 ...
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
111 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
48 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
164 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
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 $[-4, 2]$.
5
votes
2answers
181 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: ...
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), ...
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: ...
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
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. ...
-1
votes
1answer
92 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
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 ...
3
votes
1answer
108 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
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. ...
4
votes
3answers
189 views

How to solve this integration? [closed]

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

Asymptotic form of the “strange” function

I want to find the asymptotic form of this function ...
0
votes
2answers
93 views
4
votes
1answer
87 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
96 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
511 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
474 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
25 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
44 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
89 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
117 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
55 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
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
114 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
63 views

Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...