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

learn more… | top users | synonyms (3)

2
votes
1answer
71 views

Forcing Exact Outputs for Integrate [closed]

I'm trying to compute the following triple integral: ...
1
vote
1answer
41 views

Partial derivative of defined function with vector input

Background: Have written a formula for the refractive index for a glass slab (n) that depends on the variables t,a and d. Now I want to calculate for example some sort of error and I'll be needing to ...
0
votes
1answer
32 views

Boundary condition not correctly imposed for NDSolve

I notice that when plotting the below NDSolveValue ...
2
votes
1answer
75 views

an Integral that should be doable:

Integrate[Cos[\[Beta]] Exp[I z Cos[\[Beta] - \[Alpha]]], {\[Beta], 0, 2 \[Pi]},Assumptions -> z \[Element] Reals] correct answer is [ I think ]: ...
5
votes
0answers
118 views

Why don't products of Dirac deltas integrate correctly?

The integral $\int \int \ \delta(x) \delta(y) \ dx dy=1$ evaluates to 0 in Mathematica ...
2
votes
0answers
60 views

Strange Integrate messages / $RecursionLimit being ignored

Introduced in 10.1.0 The following behavior was observed in Mathematica 10.1 (Windows 64 bit) When attempting to evaluate the following integral, Mathematica outputs several messages which appear ...
0
votes
2answers
83 views

Fix my code to return a table of values

Here is a “procedural” program that we wrote in my class, implementing the rectangle rule of numerical integration: ...
27
votes
1answer
361 views

many indefinite integrals do not evaluate in 10.1, looking for the cause

Many integrals no longer evaluate in V 10.1 when they did in 10.0.2 Here are some 23 integrals as an example, that all produced results in V 10.0.2, but now all returns unevaluated! I am hoping ...
0
votes
0answers
43 views

Calculus with Mathematica, books, interesting examples [duplicate]

I'm looking for a book where I could find informations and interesting examples regarding examine functions of one variable like continuity of functions, limits, differentiability in Mathematica. I'd ...
4
votes
1answer
133 views

Mathematica does not help in this integral

I am trying to solve this integral with assumptions: ...
0
votes
0answers
35 views

Computing integral involving derivatives

I want to evaluate an expression $\int_C g(\nabla f)ds$. This is an integration along a curve $C$ in a plane given as a function of some parameter $s$: ...
0
votes
1answer
67 views

Can't obtain a closed form expression for an integral

I am trying to find the result of quite a complicated double integral. While the first part (being a Principal value integral) gave no particular problems, the second one is not providing any closed ...
8
votes
0answers
53 views

Finding simplifying substitutions for an integral involving limits and integrand

[The following is based on a William Lowell Putnam Mathematical Competition problem.] Consider the definite integral: $I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\sqrt{\log ...
2
votes
3answers
142 views

How can I get the exact value minimum of this function?

I want to find min of the function $$\frac{1}{\sqrt{2 x^2+\left(3+\sqrt{3}\right) x+3}}+\frac{1}{\sqrt{2 x^2+\left(3-\sqrt{3}\right) x+3}}+\sqrt{\frac{1}{3} \left(2 x^2+2 ...
0
votes
1answer
76 views

Four integrals, how can I expedite the calculations?

I have to calculate the following multiple integrals (4 integrals) ...
0
votes
0answers
38 views

numerical integration with parameter

Now I'm trying to integrate a function numerically. But it shows always an error message. x=y is not a valid limit of integration I know that this function ...
5
votes
2answers
363 views

How can I get the inverse of my function?

The original function is $$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$ I want to express $e^{\frac{\phi }{k t}}$ about $m$ and $f$, so I tried: ...
0
votes
1answer
60 views

PDE of real-world system, integral boundary condition

I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ...
0
votes
0answers
87 views

How can I verify double integral solution?

I have a double integral as follows \begin{equation} 1-(\int_0^\infty (\frac{Cje\cdot Cte \cdot e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)^2} + \frac{e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)}) ...
1
vote
1answer
88 views

How can I simplify a triple integral with exponentials?

I want to simplify the following triple integral with exponential terms. \begin{equation} \int_0^\infty\int_0^\infty \int_0^\infty \frac{1}{R\,G} e^{-p(1+R\,a)-q\, b \frac{1+R\, a}{1+G\, x}}\, ...
5
votes
1answer
238 views

Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
4
votes
2answers
122 views

Well-defined symbolic integral leading to ConditionalExpression

I would like to determine a closed-form expression for the following symbolic integral $$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
3
votes
3answers
59 views

Multiple integrals where the number of integrals is aribtrary

I know that I can do, say, a triple integral such as $$\int_{a_x}^{b_x}\int_{a_y}^{b_y}\int_{a_z}^{b_z}f(x,y,z)\,dz\,dy\,dx$$ with the input ...
-4
votes
1answer
48 views

Show steps to compute limit [closed]

I'm trying to use Mathematica to compute a limit, because I have no idea how to compute it by myself. The limit should be: $$\lim _{n\rightarrow \infty }\dfrac {2^{n+1}-n-2}{2^{n}}$$ Any ideas?
0
votes
1answer
58 views

Cauchy Principal Value integral- no result is obtained [closed]

I have a particular Cauchy Principal Value integral that I need to numerically solve for my thesis research. It is the following $$ ...
4
votes
2answers
246 views

Using Mathematica to confirm Bernoulli's inequality

I have several challenges that I want to confirm is true. I have chosen this one because it is rather simple (proof by induction). There are times when I do not want to spend ages trying find proofs. ...
0
votes
0answers
26 views

Use implicit differentiation to find the slope of the tangent line to the curve 4 xy^3+ 5 xy= 45 at the point ( 5 , 1 ) [duplicate]

Use implicit differentiation to find the slope of the tangent line to the curve 4 xy^3+ 5 xy= 45 at the point ( 5 , 1 )
6
votes
2answers
322 views

Convolve does not get the correct answer

Convolve[Sinc[x], Exp[-x^2], x, X] (* E^-X^2 π *) is obviously false, but why? Any suggestions ?
3
votes
3answers
90 views

How to Integrate trivial products of DiracDelta

A long while ago I was able to integrate with Mathematica: $$\int_0^1 \delta(1-x)\delta(x) f(x) \,dx = 0$$ using ...
0
votes
1answer
70 views

How to do this triple integral?

I have a triple integral which is kind of complex, and I want to use Mathematics to help me do the integral. However, when I press "Enter" and "Shift" the software get stuck. I wonder whether this ...
0
votes
2answers
85 views

Finding the equation of tangent lines where a function has a specified slope [closed]

A function is defined as f[x_] := 3x^4 + 8x^3 - 24x^2 - 48x + 19 I need to find the equation of the tangent lines at the points where the tangent line has a ...
1
vote
1answer
59 views

Integrating with assumptions and limits of integration [duplicate]

I have an integration with assumptions and limits of integration. I tried to use Mathematica to solve this problem, but I cannot get any results. ...
4
votes
2answers
390 views

Real integral giving imaginary answer

Hello I am trying to evaluate the following integral Integrate[4279/Sqrt[0.6817 + 0.3183*(1 + x)^3], {x, 0, 20}] my mathematica 9 gives me ...
-1
votes
1answer
80 views

how can use $\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$ [closed]

How can calcul $$\mathop {\lim }\limits_{x \to 0} \frac{{e^x - e^{\sin \left( x \right)} }}{{x - \sin \left( x \right)}}$$
0
votes
0answers
102 views

Mathematica can't, or won't evaluate an integral (again)

I'm relatively new to Mathematica and really need some help here to spot what's going wrong with my integration issues; Mathematica doesn't evaluate my integral, after a fair amount of time running, ...
0
votes
1answer
85 views

How to make Mathematica show intermediate steps in integral [duplicate]

I want to know how Mathematica evaluates this integral: $PV \int _ {0} ^ {i \infty} d \tau \, \frac{e^{-\frac{\tau^2}{2 M^2}}(b^2 - 3 τ^2)^2 (|b^2+\tau^2|-(b^2-\tau^2))}{\tau (\tau^2 - b^2)}$, where ...
0
votes
1answer
111 views

Solving Integro-Differential equations

I need help solving this equation. Is there a built in function that solves this type of equations? DSolve wouldn't work. Updated equation: ...
0
votes
1answer
43 views

Function to Represent Recursive Integral

I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$): $K_{i,n}\left(x\right)=\intop_{x}^{\infty}K_{i,n-1}\left(y\right)dy$ where ...
0
votes
2answers
101 views

Why does FindMinimum return 'The function value Null is not a real number'?

I am working with the following function ...
3
votes
1answer
161 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
2
votes
1answer
89 views

Calculate exact Probability of product of normal random variables

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = ...
1
vote
2answers
98 views

Differentiation of an unknown function

I have to take the partial differentiation of an unknown function. For example, take the unknown function to be $g(x)$. Then it's derivative w.r.t $x$ is $g'(x)$. By default, Mathematica ...
2
votes
0answers
49 views

Getting error messages from a Plot expression containing an integral [closed]

This should be a really simple question, but I just got confused. Plot[Integrate[x, x], {x, -5, 5}] Integrate::ilim: Invalid integration variable or limit(s) ...
-2
votes
1answer
76 views

Help me with sum [closed]

good morning $$ \begin{array}{l} \left\{ \begin{array}{l} u_0 = 1 \\ u_n = 3 - \frac{4}{{1 - v_n }} \\ \end{array} \right.\quad \\ \;v_n = \left( { - 3} \right)^{n + 1} \\ s = v_{1436} ...
3
votes
2answers
201 views

Integral does not converge (when it should)

I was looking at integrals like: Integrate[HermiteH[50, x]*Exp[-x^2], {x, 0, Infinity}] which gave me a "does not converge on $(0,\infty)$" error. On the other ...
0
votes
1answer
69 views
0
votes
1answer
69 views

Integrating spherical harmonics

I am trying to simply check the integration/normalization condition on the SperhicalHarmonic functions that are built into Mathematica. So basically, I just want to check that the following integral ...
2
votes
1answer
97 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
1
vote
1answer
58 views

Performance boost for definite integration with symbolic limits

In Mathematica, the symbolic definite integration ...
2
votes
0answers
80 views

How can I do multiple (double) integral with periodic boundary conditions?

I am trying to do a simple double integral $\int_0^l \left[\int_0^l h^3 h_{xxx}dx\right]dx$ with periodic boundary conditions $h[0,\tau]=h[l,\tau]$ $h_x[0,\tau]=h_x[l,\tau]$ ...