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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2answers
250 views

Integrating polynomial functions over polytopes with an add-on package

There is a Mathematica package to evaluate integrals over polytopes: http://library.wolfram.com/infocenter/Books/3652/ In the documentation (Functions.nb file) I ...
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1answer
168 views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
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2answers
142 views

How to calculate an improper integral

How can I find the range of the parameter a such that the improper integral Integrate[(x^(a - 1))/(1 + x), {x, 0, ∞}] ...
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3answers
105 views

How to remove the 1. when differentiating 0.5x^2

My question is very basic, When using the Differentiate functionality of Mathematica in this way: D[0.5 x^2, x] This results in: ...
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1answer
146 views

Plot[ D[Sin[x]] ] and Evaluate[] [duplicate]

Why does t = 2 Pi; Plot[D[Sin[x],x], {x,0,t}] (* Plotting the derivative of Sin[x] *) not work, but ...
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1answer
225 views

Can I take derivative of a function that represents a piece of music?

Can I take the derivative of a function that represents a piece of music? The music is given in .mp3, .midi or whatever comes in handy.
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2answers
467 views

Using Mathematica to find poles of Gamma functions

I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper: $$\int\frac{d^d ...
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1answer
146 views

Computing the volume and the curved surface area

I'm trying to compute this function $y=\frac{1}{2}e^x+\frac{1}{12}e^{-3x}$ to get the volume of the solid of revolution when the area under the curve is revolved once around the x axis. And than get ...
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1answer
92 views

How can I find the derivative of a combinatorial expression? [closed]

I want to differentiate the following equation: n = (nchoosek)*p*(1 - p)^(n - k) After differentiating my result is: ...
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2answers
89 views

How to add a condition to a formula so that it will not appear at the result? [duplicate]

Sometimes I have very long and complicated equations, when I evaulate the equations for example taking derivative or integral there will be several conditions with the answer. My question is that; is ...
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1answer
68 views

Is there a more idiomatic way to solve this implicit differentiation problem?

Here's an exercise from a calculus text by Larson and Edwards: Find the rate of change of the distance between the origin and a moving point on the graph of $y = x^2 + 1$ if $dx/dt = 2$ ...
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2answers
329 views

Integrating hat functions

I am trying to integrate a hat function for a project that I am doing and have found a method to do so but I find it sloppy. Currently I have the basis function ...
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2answers
536 views

Integral with the derivative of Dirac delta does not evaluate correctly?

Integrate[DiracDelta'[y - z] DiracDelta[x - z], {z, -Infinity, Infinity}, Assumptions -> x \[Element] Reals && x \[Element] Reals]
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2answers
148 views

How to numerically integrate this integral?

I want to integrate the function funcin (spherical coordinates). ...
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1answer
418 views

No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]

Is my input below correct? I've received no response from Mathematica. N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]] Thank ...
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3answers
61 views

Is there a way to rewrite integrals in Mathematica using u substitution?

In Mathematica, can I give it an integral and a few substitution rules and have it rewrite the integral in terms of those variables?
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1answer
75 views

A problem with “RiccatiSolve::ncsol: Cannot compute a stabilizing solution to the matrix equation ”

I have a SSM ( State Space Model ) and I want to calculate its optimum gains unisng LQOutputRegulatorGains[] command. When I run the code, it solves the equations ...
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1answer
53 views

Forcing an integral to be solved in separate terms

Using Mathematica I want to solve an integral over a function that contains both determined and undetermined parts which looks like this: ...
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1answer
91 views

Help with Computation-heavy triple integration

I'm Trying to use Mathematica to symbolically integrate a function with respect to x, y, and z. For some reason, this computation either takes about, 60s and returns the input, or takes many hours ...
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1answer
78 views

Numerical vs Symbolic Integration: Loss of precision

I am trying to integrate the following expression over the time interval $0\leq t \leq \text{period}$. ...
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2answers
147 views

Numeric mixed derivatives

In short I need NumericCalculus`ND extended to mixed partial derivatives. This can be done by nesting them, but care has to be taken to evaluate underling ND only when the parameters become numeric. ...
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1answer
95 views

Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
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1answer
210 views

Gram-Schmidt process with Hermite functions on [-1, 1]

Denote by $h_n$ the $n$-th Hermite function. $$ h_n(x) = \frac{(-1)^n }{\sqrt{2^n n! \sqrt{\pi}}} \mathrm{e}^{\frac{x^2}{2}} \frac{\mathrm{d}^n}{\mathrm{d} x^n} \mathrm{e}^{-x^2} $$ I am trying to ...
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1answer
209 views

Integrate of Heaviside Function returns an error answer

I try to evaluate an Integral of a Heaviside function, but it turns out with an erroneous output(zero). Here is my integral: ...
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1answer
263 views

NumericQ prevents evaluation at a numerical value sometimes

I set up a symbolic integral, to be evaluated only when some of the symbols have been replaced by numbers. The evaluation after assigning numbers to the symbols is still symbolic for some reason. The ...
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1answer
223 views

Integrate function without specifying limits of integration

I've been having trouble to make mathematica evaluate an integral without specifying the values of the limits of integration. I mean, if I write ...
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1answer
1k views

Given x[u,v], y[u,v], and f[x,y] how do I find D[f,x] in terms of u,v?

I have two functions x = x(u,v) and y = y(u,v). The chain rule says that for a function f(x,y), df/dx = df/du du/dx + df/dv dv/dx, and similarly df/dy = df/du du/dy + df/dv dv/dy. How do I get ...
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2answers
466 views

Why Can't Mathematica Integrate this?

I have the following problem from a textbook I am trying to integrate: So, following the directions in text, I am required to integrate each function. However, I cannot get Mathematica to integrate ...
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1answer
82 views

Sum rule in integration not working [duplicate]

I am new to Mathematica and I just tried to play around with some integrals. But the sum rule in integration doesn't work. Here a simple example: Mathematica doesn't recognize that $\int_0^h (1-f(x)) ...
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votes
1answer
69 views

Integral calculation in Mathematica [closed]

I need to calculate this integral using Mathematica: ∫ t^z * ln(t) dt from x to y with the assumptions that z is an integer and 0 < x < y This is what I'm trying to do: ...
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votes
2answers
128 views

Integral with unreliable result

I want to calculate $\int_R^1 \sqrt{r} |\cos((k+\frac{1}{2})\pi r)|dr $ and I get a result from Mathematica. Then I try to check the result putting the value of $k$ and $R$, (k=1 and R=0.5) in the ...
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votes
1answer
82 views

Defining a function that differentiates another function with rule replacement

This question is related to the question I posted here. In that question, I thought I have simplified my original problem into an equivalent concise version, but I found that it is not. So I decided ...
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2answers
57 views

Problem with using the chain rule [closed]

I have the functions w[x_] := x*Cosh[x] and x[a_] := n/k*a. I take the derivative ...
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1answer
145 views

How to the take derivatives of a parametric function? [closed]

I have a parametric curve of the form $x(t)=2t^3+3t^2-12t,\ y(t)=2t^3+3t^2+1$ How do I take the derivative of that function in Mathematica? Is there a certain function I should use?
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1answer
84 views

How to evaluate an integral involving normal distribution [closed]

I want to compute the following integral, in which 5 can be replaced by any natural number. But I found Mathematica keep running forever and cannot evaluate it. I want to ask for some help. ...
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votes
1answer
156 views

Revolve A Function Around the Y axis? [duplicate]

I am seeking to revolve the are between the functions function $d(x) = Exp(x)$ and $e(x) = 4 - x^2$ around the line $x = 2$. I am using RevolutionPlot3D, so I ...
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votes
2answers
141 views

NDSolve boundary query / Extracting values from solution

I have a function $O_{2}$ with boundary conditions $O_{2}(r_{o}) = p_{o} $ and $O_{2}(g) = O_{2}'(g) = 0$. I plot it using the solver code below; ...
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1answer
111 views

Explicit, closed formula for recursive integral as a function of the recursive parameter

This is a follow-up of this question/answer. I'm working on a recursive integral more complicated than the one on the linked question, but this one can be used as an example. I would like to obtain ...
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1answer
495 views
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1answer
98 views

How do I generate arbitrarily many integration bounds? [duplicate]

I have a multiple integral of the following form: $$\int_{-\infty}^\infty \cdots \int_{-\infty}^\infty \exp(-\sum_{i,j=0}^n x_i A_{ij} x_j) dx_1 \cdots dx_n $$ Here, $A$ is a square matrix and $x_1 ...
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votes
2answers
78 views

Obtaining a particular form of solution for an integral

When I do: Integrate [E^(-(t/\[Tau])) Cos[\[Omega] t], {t, 0, \[Infinity]}] How could I get the solution in the form: ...
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1answer
186 views
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1answer
63 views

Functions in functions

I have three functions f(x,y) , g(t) , and h(t) and somehow I have to find (d/dt)f(g(t),h(t)) where t = 0. How would I go about writing this in Mathematica? In this equation g(t) is taking place of x ...
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1answer
94 views

Solving Coulomb Integral [closed]

I am trying to solve so-called Coulomb Integral of two Gaussians: ...
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votes
1answer
42 views

Evaluation of integral [closed]

I want to evaluate an indefinite integral using the Integrate command, and I know that the answer can be written in terms of elementary functions (square roots, logs etc.) but Mathematica seems to ...
0
votes
1answer
91 views

Integrate and NIntegrate yield different results for double integral

Evaluating a double integral with bivariate normal distribution yileds widely different results depending on the method used. I define a bivariate normal distribution with {10, 3} and {8, 1.5} as ...
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votes
1answer
60 views

Integrating function can't be epressed? [closed]

Hi I have a function in a form of $$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$ The code is Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}] But it can't work ...
0
votes
1answer
50 views

Derivative of the composition of two functions

Background, this seems to work (This is manually transcribed from the program, beware of errors): J1[f_, i_] := DifferenceDelta[f[i], i]^2 D[J1[f + t v, i], t] ...
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1answer
45 views

Integral not being evaluated

I'm trying to do the following integral, but Mathematica won't evaluate it - it just spits out the actual symbollic integral (sorry I'm not sure how to copy the output into this post so it appears as ...
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1answer
62 views

One more question about Assumptions and Integrate

There are many questions about assumptions here. Many of them are problem specific. That is why I want to ask a question in the most general way. Why does Mathematica solves this ...