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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-1
votes
1answer
154 views
4
votes
2answers
285 views

Integration of a Rational Function returns RootSum[]

I am trying to solve an integral given below: Integrate[r^2/(-α r^3 + r^2 - 2 m r + Q^2), r] but since coefficients of this cubic polynomial are as parameters, ...
8
votes
4answers
395 views

Definite integral incorrectly giving a nonreal value

fixed in 10.1 (windows and Mac OS X) In Mathematica 10.0, when I enter N[Integrate[Sqrt[1+x^3],{x,-1,3}]] I get a nonreal value (i.e., the imaginary part is ...
0
votes
2answers
84 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
147 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 ...
2
votes
1answer
180 views

Complex Integration

There are some sequential functions: ...
9
votes
1answer
231 views

Suspected bug in Integrate

Bug introduced in 9.0.1 or earlier and fixed in 10.1.0 In version 10.0: ...
0
votes
1answer
176 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
109 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
77 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] ...
27
votes
2answers
348 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
0
votes
1answer
130 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: ...
7
votes
1answer
88 views

Inconsistent results for Integrate depending on irrelevant assumptions

I stumbled across this amusing issue today when doing some definite integrals: ...
3
votes
1answer
227 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 ...
1
vote
0answers
109 views

Piecewise functions Integration with symbol

I want to integrate one piecewise functions as following, ...
-3
votes
1answer
137 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
75 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
82 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.
2
votes
0answers
77 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
785 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
99 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 ...
10
votes
1answer
370 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
177 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
164 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. The equation below presents the final form ...
4
votes
1answer
321 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 ...
2
votes
1answer
140 views

Function to calculate finite difference

I wrote a function to calculate multivariate finite difference of different orders ...
1
vote
2answers
116 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 ...
5
votes
2answers
195 views

Multidimensional integral to compute the end-to-end distribution of a FENE ideal chain

How do I evaluate the mean end-to-end squared distance of a FENE ideal chain at fixed inverse temperature $\beta$ in the canonical ensemble? This quantity is defined as the mean value ...
2
votes
1answer
87 views

How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
1
vote
0answers
121 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
142 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
207 views

Power series graphs?

I would like to graph this function and its first 6 Taylor polynomials on the same axis, but I'm not sure how to start: f[x_] = Exp[x]; Plot[f[x], {x, 0, 1}]
4
votes
2answers
264 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
3answers
383 views

Negative integral of a positive function

fixed in 10.1 (windows) For a parameter $t\in (0,1)$ $Assumptions = t ∈ Reals && t > 0 && t < 1 I define an obviously positive function ...
3
votes
1answer
125 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
45 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 ...
5
votes
1answer
304 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
82 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 ...
1
vote
1answer
99 views

Computing a binomial series

How can I compute the following series: Module[{n = 10^6}, Sqrt[n] * (4^-n) * NSum[Binomial[2*n - 1, n - k]/((2 k - 1)^2 + Pi^2), {k, 1, n}]] including ...
4
votes
0answers
89 views

MacDonald formula for Modified Bessel Functions

How can I make Mathematica understand 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) } ...
6
votes
1answer
356 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
781 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" ...
0
votes
2answers
141 views

How to help MMA to simplify integrands?

MMA sometimes has to grind for LONG time on easy integrals: ...
-1
votes
3answers
267 views

Defining an alternative derivative function?

I want to calculate the derivative at a point, but I do not want to use the built-in derivative function D. I began with this definition of the derivative , ...
7
votes
2answers
868 views

Mathematica 10 cannot solve definite integral [duplicate]

Bug introduced in 10.0 and fixed in 10.0.2 Mathematica 10 fails to solve the following integral, saying that it does not converge. ...
4
votes
1answer
598 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
2answers
485 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
97 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
326 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
118 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 ...