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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0
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2answers
54 views

A simple integral operation

Evaluating the following expression results in a non-zero output FullSimplify[Integrate[2 f[x], {x,0,1}] - 2 Integrate[f[x], {x,0,1}]] I think the output should ...
1
vote
1answer
98 views

Partial differentiation mixes up variables

Consider $$ U \equiv \dot{\theta} - \theta \ ,$$ where as per usual $\dot{\theta} = \frac {d \theta}{dt}$. We then have $$ \frac {\partial U}{\partial \theta} = -1 \quad , \quad \frac {\partial ...
0
votes
0answers
46 views

Fourier Transformation of a List

As we know the FourierTransform goes a function of t ,for example, f[t] to ...
1
vote
1answer
93 views

Complex Integration

There are some sequential functions: ...
6
votes
0answers
109 views

Suspected bug in Integrate

Bug introduced in 9.0.1 or earlier and persisting through 10.0.2 or later In version 10.0: ...
0
votes
1answer
55 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
2
votes
1answer
89 views

How to check if Integrate solved the integral?

This seems something that must have been asked before, but I am not able to find something. Integrate does not return status nor throw error when it can't find antiderivative. It just returns the ...
0
votes
3answers
65 views

Listing all cubic order derivatives of a function of 4 variables

What would be the best way to list/print all cubic order derivatives of a function of 4 variables? I was thinking about iterating Derivative[i,j,k,l][func][0,0,0,0] ...
20
votes
1answer
237 views

Bug in ArcLength?

With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
-1
votes
0answers
33 views

How to use ito calculus in mathematica for multiple SDEs

I have following SDE's dS1 = mu1 S1 + sigma1 S1 dW1 dS2 = mu2 S2 + sigma2 S2 dW2 E[dW1 dW2] = rho This can be extended to multi asset case also where we have ...
0
votes
2answers
83 views

Graphic solution lagrange multiplier (cant get one)

I need to find the maxima and minim of a function. I did analytically with no problem but now I need to show in a graphic the intersection of the functions. My function is: ...
6
votes
1answer
59 views

Inconsistent results for Integrate depending on irrelevant assumptions

I stumbled across this amusing issue today when doing some definite integrals: ...
3
votes
1answer
66 views

How to perform “implicit” integration? [duplicate]

(I wasn't sure what to put for the title, so feel free to improve it if you can think of a better one.) How do I evaluate an integral that contains an unknown function of the integration variable ...
0
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0answers
43 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
-1
votes
0answers
34 views

Mathematica integrations? [duplicate]

New mathematica user here, when integrating (1+lnx)Sqrt(1+(xlnx)^2), when plugging the u and du values into the integral, how should it look exactly? Cheers, -Josh
-3
votes
1answer
98 views

Integration with mathematica? [closed]

I am very new to Mathematica. I am trying to evaluate ∫ (1+lnx)Sqrt(1+(xlnx)^2) using Mathematica. I know a substitution must be done so I have set ...
-1
votes
1answer
60 views

Taking the third derivative of: $f = (ln (x) + e^{4 (x - 1)})^{15}$? [closed]

I am VERY new to Mathematica and struggle to solve this question: Let $f = (ln (x) + e^{4 (x - 1)})^{15}$ and calculate what value $f^{(3)}(1)$ have. How would you go about to solve this in ...
0
votes
1answer
51 views

Finding the limit of powers to infinity [closed]

Limit x -> Infinity (1 - e^-x)^e^x I keep getting that the answer is 1 but according to wolfram alpha it is 1/e. Could someone show me how. Thanks.
1
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0answers
56 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
0
votes
2answers
674 views

How to find volume of an egg [closed]

I am a first time user of mathematica. I've been trying to figure out how to find the volume of a) f(x)=(ax^3 + bx^2 + cx + d)sqrt(1-x^2). I have been scouring the internet for a solution on how to ...
0
votes
1answer
84 views

How should i correct this error?

Sn = Sum[1/((k + 1)^2), {k, 1, n}] SSn = Sum[Sn*Fibonacci[n], {n, 0, m}] Limit[(1/(Fibonacci[m + 2] - 1))*SSn, m -> Infinity] Limit::ztest1: Unable to ...
6
votes
1answer
306 views

How to code around known MMa special-case failures?

Fourier Analysis and Signal Processing often require these integrals on functions f[x] that won't be known in advance. ...
1
vote
1answer
51 views

How to rotate vectors in vector plot?

I'm writing an exam for my calculus students and am seeking help with using Mathematica on a particular problem. Here's my idea: I want to give a multiple choice problem that has four choices of ...
0
votes
0answers
69 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. I have attached the code defining the ...
4
votes
1answer
174 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
-4
votes
1answer
48 views

How to Integrate [duplicate]

I have the following Table ...
-2
votes
1answer
63 views

How to integrate a table? [closed]

I have the following Table (dy/dx)={24,24.5,25,25.4} How do I proceed to interpolate the table and compute Integrate[Sqrt[1+(dy/dx)^2],{x,65,68}] ?
1
vote
2answers
69 views

Integrate full derivative

I want mathematica to do Integrate[D[f[x],x], {x,0,t}] and achieve the answer f[t]-f[0]. But Mathematica doesn't intergrate ...
0
votes
0answers
25 views

Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
1
vote
0answers
74 views

Where can I learn to use mathematica comprehensively? [duplicate]

I've heard great things about all the wonders and capabilities of mathematica. I've had the software for sometime now, but all I know how to do are simple calculations and stuff shown in the hands on ...
0
votes
1answer
46 views

Mathematica Lattice Reduce Command

I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice. I'm on chapter 3, and ran into the LatticeReduce ...
4
votes
2answers
197 views

How to force correct answers for Integrals of Cos[mx]*Cos[nx]? [duplicate]

This is a big problem if you do anything with a Fourier Series. This statement: Assuming[Element[{m, n}, Integers], Integrate[Cos[m*x]*Cos[n*x], {x, 0, 2 Pi}]] ...
7
votes
2answers
257 views

Negative integral of a positive function

For a parameter $t\in (0,1)$ $Assumptions = t ∈ Reals && t > 0 && t < 1 I define an obviously positive function $f(x)=\left| \Re ...
2
votes
1answer
100 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
0
votes
0answers
44 views

Find the maximum/ minimum of the function f(x,y,z) = x+2y+3z on the curve of intersection of the plane x-y+z = 1 and the cylinder x^2+y^2 = 1 [duplicate]

How to write the program for: Find the maximum/ minimum of the function f(x,y,z) = x+2y+3z on the curve of intersection of the plane ...
0
votes
2answers
47 views

How to calculate improper integral [closed]

Hello, How to calculate the "r" (limit) of this improper integral ?
5
votes
1answer
192 views

How can I Integrate large trigonometric expressions more efficiently?

I have a requirement to integrate some large symbolic expressions containing products of trigonometric functions. A single integration is averaging 7 minutes, and I have 2628 expressions to integrate, ...
3
votes
1answer
72 views

Integrate[] does not work when the function has an antiderivative function

This function (1 + (1 + 1/(2*Sqrt[x]))/(2*Sqrt[Sqrt[x] + x]))/(2*Sqrt[x + Sqrt[Sqrt[x] + x]]) has the antiderivative function, since ...
0
votes
1answer
45 views

Computing a binomial series

I have a simple question: how to compute the following series? Sqrt[1000000]/4^1000000 NSum[Binomial[2*1000000 - 1, 1000000 - k]/((2 k - 1)^2 + Pi^2), {k, 1, ...
1
vote
0answers
38 views

MacDonald formula for Modified Bessel Functions

Mathematica seems to not know these two integrals: $$\int_0^{\infty} e^{-x \cosh{\xi}} d\xi = K_0(x)$$ $$\int_0^{\infty} e^{-\frac{1}{2} \Big( \frac{x y}{u} + u \frac{x^2+y^2}{x y} \Big) } K_{i t}(u) ...
5
votes
1answer
277 views

How to solve this probability symbolically or numerically?

I am trying to calculate the following probability $$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$ where, $$A_i \sim \exp(\lambda), \quad S_i \sim ...
4
votes
4answers
527 views

Visualizing Line Integrals

I have a plane curve $C$ described by parametric equations $x(t)$ and $y(t)$ and a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}$. The line integral of $f$ along $C$ is the area of the "fence" ...
1
vote
0answers
66 views

integral with Re[] function, need help [closed]

I tried to compute with Wolfram Mathematica the following integral The code is ...
0
votes
0answers
51 views

Can Mathematica do this integral over $\mathbb{R}^n$?

I have the following function: $$\phi_{k,n,r}: \mathbb{R}^n \rightarrow \mathbb{R}, (x_1,…,x_n)\mapsto (1-r^{n-k}e^{\sum_{i<k}x_i})e^{\sum_{i<j}x_i-x_j}e^{(2-n)\sum_i x_i}$$. Is there any way ...
5
votes
2answers
598 views

Mathematica 10 cannot solve definite integral

Bug introduced in 10.0.0, solved in 10.0.2 Mathematica 10 fails to solve the following integral, saying that it does not converge. ...
4
votes
1answer
146 views

Integrate over piecewise function defined using /;

f[x_] := x /; x<0 f[x_] := x^2 /; x>=0 Integrate[f[x],{x,-1,1}] The above does not work (Mathematica returns it unevaluated), but the below does. ...
3
votes
1answer
181 views

How to numerically integrate this integral

I am unable to do this definite integral in Mathematica 9. Is there any command so that I can get the numerical value of the above integration? Code: ...
0
votes
2answers
54 views

Derivative in function form

I have a function in mathematica defined as b[n_, x_] := x^n/n!/\!\(\*UnderoverscriptBox[\(\[Sum]\), \(k = n\), \(\[Infinity]\)]\*FractionBox[\(x^k\), \(k!\)]\) ...
2
votes
1answer
69 views

Using Integrate to define a function

I'd like to define a function by way of the output of a definite integral with symbolic bounds. For instance, F[m_,k_] := Integrate[x,{x,m,k}] would define ...