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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7
votes
1answer
68 views

Inconsistent results for Integrate depending on irrelevant assumptions

I stumbled across this amusing issue today when doing some definite integrals: ...
3
votes
1answer
73 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
votes
0answers
49 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
-3
votes
1answer
106 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
65 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
54 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
vote
0answers
61 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
692 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
85 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
317 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
64 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
76 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
207 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
73 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
74 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
36 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
85 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
52 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
208 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
282 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
103 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
53 views

How to calculate improper integral [closed]

Hello, How to calculate the "r" (limit) of this improper integral ?
5
votes
1answer
217 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
77 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
50 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
44 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
289 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
566 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
68 views

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

I tried to compute with Wolfram Mathematica the following integral The code is ...
0
votes
0answers
54 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
631 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
282 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
211 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
65 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
82 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 ...
0
votes
1answer
112 views

Tough Calculation, novice mathematica user

I have an equation, that I've been calling $b_N(x)$ that satisfies the following identity: $$-Nb_N(x)^2=(x-N)b_N(x)+xb_N'(x)$$ where $b_N'(x)$ is the first derivative. I take the derivative then of ...
0
votes
1answer
63 views

Multidimensional NIntegrate problem of the function decaying as 1/x^2

The function I am trying to integrate is more complicated but I can simply write the function as (I had made a typo error, sorry. The '+' sign in front of the r should be '-'): $f(\omega ) = \int ...
0
votes
1answer
48 views

Negative Infinity limit [closed]

As a beginner I am trying various functions of mathematica to practice. I am at the limit function. I am trying this ...
0
votes
1answer
122 views

Integrating elements from matrix

oI'm kinda new at using Mathematica. What I'm trying to do is create a matrix with elements inside. ...
1
vote
1answer
90 views

Why Abs[Infinity] is an element of the real numbers

Element[Abs[Infinity], Complexes] returns False, that's right. But ...
2
votes
1answer
88 views

Hilbert transform of density of states [closed]

I am trying to evaluate analytical integration over density of states, for example G(Z)=int[f(x)/z-x,{x,x1,x2}] , where ...
4
votes
1answer
203 views

Problem on limit involving complex numbers

I have $${\frac{(6 k+1)^{k}}{(2 k+5)^{k}}}*(z-2 i)^k$$ and I need to find it's limit for $k$ approaching infinity. ...
14
votes
1answer
242 views

Why do big-O terms disappear in definite integrals since Mathematica 9?

In Mathematica 8, when I computed the following input: Integrate[Series[Cos[x], {x, 0, 2}], {x, 0, a}] Mathematica returned an expression that had a O[a^4] in ...
1
vote
0answers
46 views

Order of integration resolves “Indeterminate expression encountered.”

Bug introduced in 10.0.0 and fixed in 10.0.1 Today I came across the following integral: ...
1
vote
2answers
110 views

Integration over a (non-parametric) curve defined by indicator function

I want to integrate the real function myFun defined on a 2D plane over the line locus, defined as the solution of a set of ...
5
votes
2answers
179 views

Unexpected Integration Constant [closed]

Why does this integration Integrate[15-30x+6x^2-1/(x+5),x] return 700 as integration constant? If we make a slight modification ...
0
votes
0answers
82 views

Mathematica Integrate implicit assumptions returns a function not defined in some points while NIntegrate performs integration safely

Hi guys i'm performing a standard integration with mathematica routine Integrate, the function i'm integrating is the following: ...
2
votes
4answers
165 views

Problem in finding the numerical maximum

I need to find the numerical maxima of the function $$i(s)=\bigg[ \frac{\sin{50\pi (\cos s+1)}}{\sin{10\pi (\cos s+1)}} \bigg] ^2$$ Or in the mathematica input form: ...