Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.

learn more… | top users | synonyms

0
votes
1answer
56 views

How to calculate the derivative at a point of a non-integrable multivariable function?

I want to integrate this function with respect to θ1 and then take the derivative of that function with respect to n. Since the ...
0
votes
0answers
29 views

Why the plot of derivate to integrate is not same with integrate to derivate? [closed]

ListPlot[Table[-((2 x)/(1 + x^2)^2), {x, -2 Pi, 2 Pi, 0.02}], PlotRange -> All] (*1*) We know that ...
0
votes
0answers
26 views

Multiple numerical integrations and green's functions propagation of the solution

I have to solve a system of equations where the coefficients have to be computed from numerical integrations. My problem is that my codes is to extremely slow because I each time that it has to ...
0
votes
0answers
51 views

Solving Fredholm equation of the 2nd kind

While I was using the code from here to solve this integral equation: ...
0
votes
0answers
64 views

Solving system of Fredholm integral equations of the second kind

How can we generalize the code previously introduced to solve the Fredholm equation of the second kind to the case of a system of Fredholm integral equations of the second kind? $$ ...
3
votes
2answers
55 views

Solving an integral equation for upper boundary

I am reading a paper on High Harmonics Generation (HHG) and a Lewenstein model The paper is here. I would like to reproduce some results but I am stuck at the following problem. I have: ...
1
vote
1answer
340 views

How to code the following in Mathematica

How do I get the following into Mathematica, solving for a: $$ 0.7 = 1 - \frac{2}{a} \times [ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1} dx + \frac{a}{6} - 1] $$
0
votes
1answer
72 views

Integrating high oscillatory function - triple integral - error message

I am working in a triple integral, but the second integral (qQ) and the first too ( aA ) is a oscillatory funcion. The third integral ( os11 ) is like a gaussian, and is easy to integrate. i am ...
1
vote
0answers
55 views

FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
0
votes
1answer
119 views

Solve a function to find the optimum value of parameter in mathematica [duplicate]

I have a complicated function as shown It doesn't have a standard integration as far as I know. Now, numerical integration of the left hand side function over a set of points gives the right hand ...
2
votes
0answers
43 views

NDSolve with NIntegrate [duplicate]

I'm new to Mathematica and I'm trying to use it to solve some equation like: NDSolve[x'[t]+NIntegrate[x[tau],{tau,0,t}]==20,x,{t,0,10}] But it keeps giving me ...
1
vote
0answers
155 views

Numerical solution to integral equation

I have an integral equation where one factor $f(t)$ in the integrand is defined in terms of an integral equation where it is again a factor. $\quad \quad y[t]=\int _0^tf[\tau ]g[t-\tau ]d\tau + ...
8
votes
2answers
461 views

How to solve the differential equation with Duhamel's integral?

How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve, but failed: ...
2
votes
1answer
183 views

Integral equation

I'm trying to solve the following integral equation: Integrate[-k/2 Exp[-k Abs[x-z]] f[x], {x,0,d}] == a f[z] Differentiating twice with respect to z should ...
0
votes
0answers
67 views

Solving a nonlinear equation involving convolution

I consider the following functional : $\psi(u,v)= -u(1-v)(1-\alpha k * v) + \epsilon v (\alpha k * v)$, where $k(x)$ is a smooth kernel with $\int |k| = 1$ and $\int k_+ = \alpha \in ]0,1[$, $u(x), ...
0
votes
0answers
58 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
0
votes
1answer
60 views

Problems with a constant term in an Integrate command

When asking Mathematica to integrate a function with Integrate, I'm getting drastically different results depending on whether I have a proportionality constant ...
1
vote
2answers
162 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
1
vote
1answer
122 views

Quantum Physics question [closed]

I'm not sure if anyone here would be able to help me. But if you know a more appropriate place where I could ask for help, please let me know. So here's the question: And here's my attempt at ...
-1
votes
1answer
140 views

Center of gravity of a cylinder in 3D space [closed]

am trying to find the center of gravity coordinates of a cylinder(x,y,z coordinates). however,I cannot figure it out using the triple integral method especially when it comes to the integral bounds. ...
0
votes
1answer
170 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: ...
2
votes
1answer
180 views

Complex Integration

There are some sequential functions: ...
5
votes
1answer
164 views

Solve a differential equation with an integral inside?

I am trying to solve this differential equation in Mathematica: y'[t]+integral from 0 to t of y[x]dx =e^(-t) where y[0]=0. Is this possible?
0
votes
2answers
58 views

Simplify integration result with conditions

Let's say I have integral Integrate[1/(1 + (f^2/B^2)), {f, 0, Infinity}] The result is $$\text{ConditionalExpression}\left[\frac{\pi }{2 ...
0
votes
1answer
102 views

Mathematica answers `Solve[Integrate[f, x] == x^4, f]` wrong [closed]

The input Solve[Integrate[f, x] == x^4, f] ouputs {{f -> x^3}} Why?
4
votes
1answer
319 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
1
vote
2answers
124 views

Output of NIntegrate depends on MaxRecursion

I have an integral in this form: ...
2
votes
0answers
182 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
4
votes
0answers
88 views

MacDonald formula for Modified Bessel Functions

How can I make Mathematica understand these two integrals? $$\int_0^{\infty} e^{-x \cosh{\xi}} d\xi = K_0(x)$$ $$\int_0^{\infty} e^{-\frac{1}{2} \Big( \frac{x y}{u} + u \frac{x^2+y^2}{x y} \Big) } ...
1
vote
1answer
91 views

symbolic integration of product of hankel function and trignometric function

I want to perform the following integration. my function is : r*cos(r)hankel(0,kr) i want to integrate from 0->pi , and want to get the expression in terms of k. I used this command ...
0
votes
1answer
164 views
4
votes
2answers
171 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
1
vote
0answers
140 views

PDE with Integral constraint

I am trying to solve the Non-linear Schrodinger equation $-\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0$ where $r \in \Omega$ In a square domain ($(x,y) \in \Omega$ where $\Omega=[0,1]\times ...
1
vote
1answer
512 views

Solving Fredholm Equation of the first kind [duplicate]

I want to numerically solve Fredholm integral equations of the first kind, equations of the form $$g(t)=\int_a^b K(t,s)f(s)\,\mathrm{d}s$$ where we know the functions $K(t,s)$ and $g(t)$ and seek to ...
3
votes
0answers
354 views

Solve integral equation for upper bound

I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: ...
1
vote
1answer
123 views

Is this integral solvable?

I am trying to solve the below mentioned integral. Is it possible to solve this with mathematica. If not, can I get an approximation for this by introducting the variable not to take certain values ? ...
6
votes
3answers
405 views

Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

fixed in 10.0.2 Update I have tried like these. I think there is a bug. ...
4
votes
2answers
68 views

DSolve results not what expected

I have the following formula: s'[t] == 230.94 Tan[0.914743 - 0.138564 t] When I solve this by hand I get: ...
1
vote
0answers
103 views

Long running time

I gave this data as input: ...
0
votes
1answer
122 views

Problem with integral equations

I have solved an integral equation with the following methods: ...
4
votes
1answer
383 views

Fredholm integral equation of the second kind with kernel containing Bessel and Struve functions

I need to solve this Fredholm integral equation of the second kind: f[s]+integrate[f[t] K[s,t],{t,0,1}]=s where ...
1
vote
2answers
82 views

Integral too slow and with conditionals

When I try to solve this integral: $$\int_{-a}^a \frac{x}{\left(x^2+y^2\right)^{3/2}} \, dy$$ it's return ...
0
votes
1answer
103 views

Calculate integral in limit of very large coefficient

How I can calculate following integrals for large values $\alpha$ in Mathematica: $$ I_1 =\int_{0}^{y} \exp\left(\, -\alpha \sqrt{x(1-x)}\,\right)\, {\rm d}x $$ $$ I_2 =\int_{0}^{y} \exp\left(\, ...
2
votes
1answer
117 views

How to solve an operator form of an integral equation by iteration method?

How I can obtain the $n^{th}$ approximation of the following Operator form integral equation? $F(t)=A(t)+\int_0^tds B(s)F(s)$, where $A(t)=\bigg{(}\begin{matrix}t&0\\Cos(t)&1 ...
4
votes
3answers
438 views

How to solve an integral equation by iteration method? [duplicate]

How I can obtain $n^{th}$ approximation of the following equation $f(t)=t+\int_0^tds f(s)$ by iteration method?
0
votes
1answer
75 views

Compute integral symbolically

I want to compute the following integral: ...
2
votes
2answers
407 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
-3
votes
1answer
117 views

Finding integral bounds

i have this integral shown below is equal to 1, and i need to find "a" on mathematica, but I'm not sure how. integral (from 0 to a) sqrt((-50.8938 sin(8.4823 t))^2+(4-11.3097 sin(11.3097 t))^2) dt = ...
0
votes
1answer
151 views

How to calculate definite integral when boundary is a limit?

Integrate[Log[x]/(1-x)^2,{x,eta,Infinity}] The conditions are eta>0, and eta->1, how ...