# Questions tagged [calculus-and-analysis]

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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### Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
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As an exercise (pertaining to my posting Perform a constrained integration over $[-1,1]^6--yielding a "separability probability"), I issued the command ... 2answers 68 views ### Is that a bug in Integrate? Why does the result of Integrate become negative? ... 1answer 86 views ### Write a function areaPerimeter[f,g,x] [closed] Write a function areaPerimeter[f,g,x] which takes as input two polynomials f and g depending on the variable x, and does the following. If the curves y=f(x) and y=g(x) intersect at exactly two ... 2answers 124 views ### How to get details about how Mathematica did a definite Integral Assuming[{Element[S, Reals],S>0},Integrate[Exp[-I*S*w]/(w^2 + 1)^(3/2) ,{w, 0, Infinity}]] gets ... 1answer 72 views ### Why is my integral not being evaluated? I am trying to integrate a function Gamma, but the output returns the input. I have the following code: ... 1answer 138 views ### To solve self consistent equations by simultaneously plotting them How can we solve a pair of equations that have to be solved self-consistently (even by plotting them simultaneously) . ... 0answers 59 views ### Perform a constrained integration over$[-1,1]^6--yielding a “separability probability”

To begin with, I have a set of three positivity constraints (ensuring the positivity of a certain (twelve-parameter) $6 \times 6$ "density matrix", denoted in the standard manner as $\rho$, namely, <...
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### Stokes theorem in Mathematica

I came across this problem in calculus. It makes a handwavy sense with the explanation provided. I have tried to prove it in MMA: ...
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### Approximate/estimate the ratio of two multidimensional constrained integrals

I have a hypothesis that a certain "qubit-qutrit separability probability" should assume the value $\frac{5}{3} \left(112 \pi ^2-1105\right) \approx 0.659488$. In its initial formulation, this is a ...
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### What is the fastest way of doing one integral in Mathematica?

I want to compute the following numerical integral in Mathematica $\int_0^L dy \int_0^y d \bar{y} f(y,\bar{y}),$ where $f(y,\bar{y})$ is a very complicated function. I show my code below where the ...
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### Modify a parameter value while solving a partial derivative

I'm currently trying to do a sensitivity analysis on a variable R0 (as defined below). This sensitivity analysis aims to determine what impact has the variation of ...
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### How do I divide an integral into parts and sum the total?

I have an exercise looking like this: Analyze the integral $4\int_{0}^{1} \sqrt{1-x^2} \, \mathrm{d} x$ numerically by deviding the interval ${]0,1[}$ into three equal parts, then summarize the ...
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### Identifying total derivatives

I would like to identify which terms in my expression are a total derivative and which ones are not. For expressions in which all terms are a total derivative, one can simply use integrate to find ...
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### Derivative of an interpolated function

I am trying to take the derivative of an interpolated function. I am given the function values and the derivatives at some irregular points. Here is my minimal working example to reproduce the error: ...
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### Second Derivative in MMA [closed]

I would like to ask, why the following second derivative is wrong in MMA ...
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### how to linearize an equation? [closed]

How does one linearize this equation?
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### Finding tangents and curvature of a parametric curve in 3D [duplicate]

I am in a calculus 3 class and cannot figure out how to get Mathematica to solve for unit tangent, normal tangent, binormal tangent, and curvature without getting a supper messy result. This is the ...
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### Symbolic perturbation expansion for quantum mechanics using Hellmann-Feynman derivaties

I am interested in some quantum mechanical perturbation expansion for energies. Actually I want to implement these terms $E_n^{(k)}$. As is stated below one can do that using CAS. I would be ...
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### Integrating function with /; in its definition

why f[x_ /; x>=0]:=x; Integrate[f[x] ,{x,0,2 Pi}] return unevaluated? Notice that the above definition of f[x] works OK ...
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### How to use Mathematica to do a complex integrate with poles in real axis?

I want to use Mathematica to compute the following complex integral: Integrate[Exp[I z ] 1/z, {z, -Infinity, Infinity}] Mathematica reports that it does not ...
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### Find area under real part of complex curve without numerically integrating

I have a function defined within the domain 0<=x<=2*Pi. f = Cos[x] * (a - 1 - r*Cos[x])^1.5 on the domain: ArcCos[(a-1)/r] < x < 2*Pi-ArcCos[(a-1)/r] f = 0 elsewhere 'a' and 'r' are ...
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### How do I draw a function along with a particular tangent line at a specific point? [duplicate]

I would like to draw a function (x/x^2+1), and at a certain point, i'd like to draw a dot along with the tangent line at that specific point. what I have tried is the following: ...
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### Piecewise function inside Integrate - Wrong result

I tried to evaluate the following integral: ...