# Tagged Questions

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

127 views

### Improper mutiple integral

I would like to solve the following integral: ...
819 views

### Double integral over a parallelogram

Problem: Evaluate the following double integral $$\int \!\!\! \int_D (14 x^2+61 xy+42 y^2)^{3} \, dxdy$$ where $D$ is a parallelogram between these four lines: $2x+7y=6$, $2x+7 y=-6$, $7x+6 y=6$ and ...
461 views

### A Bessel & Struve functions related integral

I try to numerically compute this integral and I don't figure out why on earth Mathematica is not able to do it. Is my input correct? Does it possibly have a closed form? ...
174 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: ...
246 views

### Another fractional part related question

Having known the fact that the evaluation of the integrals containing fractional parts often contains errors, I wonder if the integral below possibly evaluates to $0.7$ or this is just a coincidence ...
587 views

### Calculating electrostatic potential from arbitrary charge density

In electrostatics, one often desires to know the electrostatic potential generated from the outside of a charge distribution; however, I am interested in finding the electrostatic potential inside of ...
172 views

### Help with finding solution for utility function [closed]

I'm brand new to Mathematica and having trouble finding a solution for Lh based on the first order condition. I'm not sure if it is something I'm doing in Mathematica or something wrong with the ...
299 views

### Revolving the area between two functions about an axis

I'm trying to graph the revolution of the area between two functions about an axis, but I'm new to Mathematica, and not sure how to proceed. My area is defined by ...
484 views

### Using units and piecewise functions in Integrate

For simple cases, Quantities appear to be handled well by Integrate: ...
493 views

### Replace rule with function? Derivatives don't evaluate

Say I have an expression (call it expr) involving a function, f[x]. I'd like to be able to evaluate that for a particular choice of ...
47 views

### Showing result of derivative and other functions [closed]

I have a problem with my Mathematica 7.0 When I write: Derivative[x^2, x] Mathematica returns as result : Derivative[x^2, x] ...
313 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; ...
65 views

### Different integral when used with assumptions

I want to calculate an integral, but Mathematica gives me different results if I am more specific with the Assumptions option of ...
304 views

### An integral with a fractional part in 3 dimensions

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
138 views

### Need to take infinite sum of residues, is there a way to choose the order of operations for ReleaseHold?

I'm computing an infinite sum of residues. I want to do something like this: ...
210 views

### Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...
334 views

### Integral over squared Hermite polynomial

I would like to calculate the uncertainty of the nth Eigenstate of a 1-dim harmonic oscillator. To obtain the result I have to solve the integral $$\int_{-\infty}^{\infty} \psi^* x^2 \psi \:dx$$ ...
256 views

### Complex limit gives wrong answer

I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...
392 views

### Incorrect value of infinite sum

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum: N[Sum[((-1)^n)/(n - (-1)^n), {n, 1, Infinity}]] (* 0.700059 *) ...
266 views

### Triple series - evaluation delayed

Trying to figure out if the infinite triple series has a nice closed form. It seems Mathematica is unable to help us here. Numerically, things remain the same, no response. Could you help? ...
4k views

### How to plot and find the volume of a solid?

How to plot and find the volume of the solid enclosed between the paraboloid z=5(x^2+y^2) and z=6-7x^2-y^2 And the answer of ...
303 views

### Limit won't compute

Does anyone know why the limit: ...
106 views

### Asymptotics of sum of binomials

I would like to find the asymptotics of Sum[Binomial[n,i]*1/i^((n+1)/2),{i,1,n}] I saw Find asymptotics of Sum[2^i*Binomial[n-i-1,2*n/3-1],{i,0,n/3}] but I can'...
542 views

### No response to an infinite limit

Trying to compute this limit, things seem to get frozen, even for hours. What would you recommend to fastly compute it? ...
3k views

### How to find the area between two curves

Find the area between y = 1 - x/π and y = Sin[x]. Here is what I have typed in so far into Mathematica: ...
749 views

### Problem with numerical evaluation of analytically solved integral, solution way off

The following command in Version 9.0.1: N[Integrate[x^50*Sin[x], {x, 0, 1}]] gives $1.4615\times 10^{48}$ which is way off from the correct solution which is ...
183 views

### How can I get the limit of a certain infinite product?

A first look at it suggests the fact the limit is precisely $1$. To check that I tried Mathematica, but no output so far. Most probably it converges very slowly. Is there any way to get the limit? <...
298 views

257 views

### Integrating a BesselJ integrand to obtain the same result as Maple 16

I would like to check the following integration: Integrate[y Integrate[1/x BesselJ[1, x Exp[I π/4]] BesselJ[1, x Exp[-I π/4]], {x, 0, y}], {y, 0, r}] ...
260 views

### Can Mathematica (or its extensions) do integration following Risch algorithm?

I wonder whether there are option for indefinite integration in Mathematica that alow to choose the algorithm? Is there an option to use this algorithm in Mathematica?
212 views

### Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
166 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 ...
117 views

### Integrate and ConditionalExpression Output

I am integrating some difficult functions and using the conditional output to place bounds on parameters to ensure integrability, but it seems that not all of the conditions are being returned. The ...
59 views

### limit calculation step by step [duplicate]

I calculate such limit with Mathematica: ...
4k views

### How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
462 views

### Limit of a complex function

Can someone show me how to find the limit of a complex function? Example: z1 = 3 + 4*I some_function[z] = z * z1 Set-up: ...
280 views

### Why the result by hand is different from the built-in DSolve?

Yesterday, I used Mathematica to solve a differential equation using the built-in command DSolve[]: ...
194 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: ...
198 views

### Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
1k views

Sorry if this is a duplicate, I've searched how to do this to no avail. What I'd like to do is a function that integrates by parts $n$ times, i.e $$\int u(x) v(x) dx = u \left(\textstyle{\int}v\... 1answer 1k views ### Integral of Lorentzian yields different results depending on when parameter assigments are made I'm evaluating the integral of a Lorentzian, which I know equals one. First I define the function and evaluate the integral in two slightly different ways. Surprisingly, I do not get the right answer ... 2answers 3k views ### Paths integrals in the complex plane I can't find how to calculate path integrals of complex functions in the complex plane. For example:$$\oint_{\mid z \mid =2}\frac{1-e^z+z}{z^3 (z-1)^2}dz
I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...