# Tagged Questions

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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### How do I numerically evaluate and plot the Fabius function?

The Fabius function is a well-known example in analysis of a non-analytic function that is infinitely differentiable. I want to be able to numerically evaluate the function for any real argument, as ...
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### Infinite Sum - Result not correct for all cases?

Evaluating the Sum Sum[a^i, {i, ∞}] yields -(a/(-1 + a)) which obviously only holds ...
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### Make integration/ plot run faster? (takes hours)

I am using Mathematica 10.0.2.0. Here is the code I am working with: ...
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### What is wrong with my formulas for a mathematical model of a double pendulum? [on hold]

I wanted to create a computer simulation on Matlab, using a model for a pendulum from this study (A double pendulum model of tennis strokes. Rod Cross. Uni of Sydney, 2006) - Link I wanted to use the ...
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### Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
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### Can this expression be calculated symbolically?

I want to do definite integration of the following expression ...
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### Curve fitting with this modified integrated log-normal function and extracting fitted?

The data to be fitted is for y vs x. We have y and x points. We do not have data for w. In fact, w variable is being varied during integration from 1e-9 to 100e-9. The fitting parameters are Ms,sigma,...
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### Incorrect result when integrating

Mathematica 10.4.1.0 produces Integrate[ Log[1 + 2 a*Cos[2 x] + a^2]*Sin[x]^2, {x, 0, Pi/2}, Assumptions -> a > 1 ] ...
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### Is it possible to “pretty print” my input integral in Mathematica like Wolfram|Alpha does?

With Wolfram|Alpha, if I enter: Integrate[r^3, {t, 0, 2Pi}, {r, 0, 2}, {z, r^2, 4}] Wolfram|Alpha will pretty print my input like so: Which is very readable, ...
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### How to find the derivative value at $(\pi,0)$ for this implicit function $n$ times?

I am trying to take the implicit derivative at $\sin(x+y)+\sin(x)=y$ and substitute $x=\pi$ and $y=0$ at least 6-7 times since I need to find the Taylor series for this function. Since I barely ...
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### Rule for derivatives

I have a differential equation of the form $$f'(x)=g(x,f(x))$$ (where $g$ is has a known explicit form, e.g. $x f(x)$) and I have an expression which contains several derivatives of $f$. I want to ...
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### Differentiation and series expansion of dot product - inconsistent results

If I differentiate a dot product, I get the result I expect D[a.b[x], x] (* a.b'[x] *) However, a series expansion of the same expression gives a very different ...
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### Cauchy integration [closed]

I am evaluating Integrate[1/(1 + 3*cosin(x)*cosin(x)), {x, -Pi, Pi}] in Mathematica, which should give me Pi, but instead I ...
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### Setting derivative of function equal to 0 at x=0 using UpValues

I'm trying to set the derivative of a function to zero at a specified point. This will act as an initial condition for an algorithm I'm writing: so I'm specifying the value of the function at x=0, and ...
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### Constructing a root solution diagram (not to tell bifurcation)

Suppose I have a third order equation depending of one parameter say .5 4 x (1 - x) (x - .5) - .5 m x^2 where m the parameter. Obviously there are 3 roots for ...
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### Integrate over a piecewise function [closed]

I want to calculate the indefinite Integral of $$f(x)=\begin{cases} 2x\cos(\frac{1}{x})& \text{ if } x\ne 0 \\ 0& \text{ if } x=0 \end{cases}.$$ I use the following code: ...
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### How can I solve this integration numerically? [closed]

how can I integrate this function numerically w.r.t r from 1 to 8, the function is as, ...
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### How to define a function that is related to derivative of Jacobi theta function

I would like to make 3D plot of the following function. ...
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### NIntegrate and Integrate seem to over-estimate an integral involving a sharp Lorentzian (Cauchy) distribution

I am trying to do a numerical integral with NIntegrate, but it seems that I get a bigger number than I should. The integral is fairly simple: ...
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### How is Integrate Implemented? [duplicate]

At the end of this 90 minute lecture by Stephen Wolfram on the history of the development of Mathematica, Wolfram takes questions from the audience. One of those questions asked how the ...