# Tagged Questions

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.

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### A problem with the Gauss Kronrod quadrature

I take the risk to ask a weird question but I wonder If i miss something. In the very complete answer to How to solve a non-linear integral equation? How to solve a non-linear integral equation? ...
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### NSolve on a function with NIntegrate

I have a function defined with an NIntegrate. The function is of x,y,z, integrated across t: ...
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I am trying to numerically solve this Volterra type integral equation. The equation I'm plugging in is a simplified version of We will take $H(\eta')$ and $q(\eta)$ to be 1 for now. $\mu$ is = $\... 1answer 95 views ### How to solve a system of integral equations [closed] I am trying to solve a system of equations as follows... f1[t]/3 == (1/3)[Integrate[f3[t], t]] f1[t]/(6/5) == Integrate[f2[t], t] f3[t] == Integrate[f1[t], t] I ... 2answers 78 views ### Integral equation solving So there is this equation that I have to numerically solve for T: Q/(3nRT) = f(T/300) - f(T/77) Here Q = 920.364, n = 0.24, R = 8.314 while f is defined as the ... 1answer 62 views ### How do I solve a nonlinear Fredholm integral equation?$u(x)= 1/3+\int_{0}^{1}x\,t\sqrt{u(t)}\,dt$u[x] == 1/3 + Integrate[x t Sqrt[u[t]], {t, 0, 1}] Any ideas on how to treat such a problem with Mathematica ... 0answers 42 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 ... 0answers 103 views ### Solving Fredholm equation of the 2nd kind While I was using the code from here to solve this integral equation: ... 0answers 101 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? $$f_{1}(x)-\lambda_{... 2answers 73 views ### Solving an integral equation for upper boundary I am reading a paper on High Harmonics Generation (HHG) and a Lewenstein model The paper is here. I would like to reproduce some results but I am stuck at the following problem. I have:$$p(\tau_b,\... 0answers 59 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 ... 1answer 135 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 ... 0answers 47 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 ... 0answers 180 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.$\quad \quad y[t]=\int _0^tf[\tau ]g[t-\tau ]d\tau + h[t]$... 2answers 577 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: ... 1answer 195 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 ... 0answers 61 views ### Integro differential eq boundary difficulties I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ... 1answer 69 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 ... 2answers 201 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. ... 1answer 137 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 ... 1answer 189 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. ... 1answer 283 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: ... 1answer 185 views ### Complex Integration There are some sequential functions: ... 1answer 119 views ### Mathematica can't solve simple force-generated-by-cuboidal-planet integral? ... 1answer 191 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? 2answers 66 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 $$\text{ConditionalExpression}\left[\frac{\pi }{2 \sqrt{\frac{1}{B^2}}},\... 1answer 414 views ### How to solve this Integral equation D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-Î´)*x[t - Î´]/5^t, {Î´, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ... 2answers 150 views ### Output of NIntegrate depends on MaxRecursion I have an integral in this form: ... 0answers 200 views ### Volterra integral equation I have to find an approximate numerical solution for the equation$$ 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))$$... 1answer 101 views ### symbolic integration of product of hankel function and trignometric function I want to perform the following integration. my function is : r*cos(r)hankel(0,kr) i want to integrate from 0->pi , and want to get the expression in terms of k. I used this command ... 1answer 202 views ### Integration not working, can I find a closed form? I have tried: ... 2answers 191 views ### Compute the average distance from the base of a rectangular pyramid to its apex How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ... 0answers 177 views ### PDE with Integral constraint I am trying to solve the Non-linear Schrodinger equation -\Delta \psi(r) + \psi(r) - |\psi(r)|^2\psi(r) = 0 where r \in \Omega In a square domain ((x,y) \in \Omega where \Omega=[0,1]\times [0,... 1answer 624 views ### Solving Fredholm Equation of the first kind [duplicate] I want to numerically solve Fredholm integral equations of the first kind, equations of the form$$g(t)=\int_a^b K(t,s)f(s)\,\mathrm{d}s$$where we know the functions K(t,s) and g(t) and seek to ... 0answers 422 views ### Solve integral equation for upper bound I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: f[t_] = Sqrt[1 + E^(-2 t)] ... 1answer 125 views ### Is this integral solvable? I am trying to solve the below mentioned integral. Is it possible to solve this with mathematica. If not, can I get an approximation for this by introducting the variable not to take certain values ? ... 3answers 425 views ### Different results of a definite integral \int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx fixed in 10.0.2 Update I have tried like these. I think there is a bug. ... 2answers 70 views ### DSolve results not what expected I have the following formula: s'[t] == 230.94 Tan[0.914743 - 0.138564 t] When I solve this by hand I get: ... 0answers 118 views ### Long running time I gave this data as input: ... 1answer 126 views ### Problem with integral equations I have solved an integral equation with the following methods: ... 1answer 458 views ### Fredholm integral equation of the second kind with kernel containing Bessel and Struve functions I need to solve this Fredholm integral equation of the second kind: f[s]+integrate[f[t] K[s,t],{t,0,1}]=s where 0<=s<=1... 2answers 82 views ### Integral too slow and with conditionals When I try to solve this integral:$$\int_{-a}^a \frac{x}{\left(x^2+y^2\right)^{3/2}} \, dy$$it's return ... 1answer 113 views ### Calculate integral in limit of very large coefficient How I can calculate following integrals for large values \alpha in Mathematica:$$ I_1 =\int_{0}^{y} \exp\left(\, -\alpha \sqrt{x(1-x)}\,\right)\, {\rm d}x  I_2 =\int_{0}^{y} \exp\left(\, -\... 1answer 127 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 \end{matrix}\...
How I can obtain $n^{th}$ approximation of the following equation $f(t)=t+\int_0^tds f(s)$ by iteration method?