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0
votes
1answer
40 views

Get rid of Error Function: How to get rid of sequential appearances of error function?

We have a function as e[t_] :=(E^(-t^2)) Cos[0.1 t] and we must evaluate below integration (However I used the variable x ...
-2
votes
1answer
58 views

How to integrate a generic integral? [on hold]

I'm trying to integrate this between $0$ and $T/4$: $$\frac{2}{T}V\int{Cos(wt)dt}$$ I use this in Mathematica: $$\frac{2}{T}(\text{Integrate}[V\int \text{Cos}[\text{wt}] \, dt,\{t,0,T/4\}])$$ But ...
-2
votes
0answers
20 views

Writing an integral for a bounded volume [on hold]

Good day folks! I'm trying to write an integral which could represent the volume of the shaded area below. However my integral calculus is quite poor, so I need some help on that equation. I ...
5
votes
1answer
86 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
23 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
69 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
173 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
68 views

Output of NIntegrate depends on MaxRecursion

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

Can Mathematica do this integral over $\mathbb{R}^n$?

I have the following function: $$\phi_{k,n,r}: \mathbb{R}^n \rightarrow \mathbb{R}, (x_1,…,x_n)\mapsto (1-r^{n-k}e^{\sum_{i<k}x_i})e^{\sum_{i<j}x_i-x_j}e^{(2-n)\sum_i x_i}$$. Is there any way ...
1
vote
1answer
66 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
89 views
4
votes
2answers
131 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
63 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
118 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 ...
2
votes
0answers
116 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
104 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 ? ...
5
votes
3answers
320 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. ...
2
votes
2answers
139 views

Integration of piecewise function

I'm trying to understand why Mathematica is not evaluating a piecewise function, while it's able to evaluate each of the regions separately. This fails: ...
4
votes
2answers
56 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: ...
0
votes
0answers
75 views

Problem solving a Fredholm integral equation

Based on the algorithm by PlatoManiac presented here Integral equation numerical solution with NDSolve I am solving a Fredholm integral equation with the following constants and arguments: ...
1
vote
0answers
70 views

Long running time

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

Problem with integral equations

I have solved an integral equation with the following methods: ...
3
votes
1answer
189 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
73 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
74 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(\, ...
1
vote
1answer
99 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
211 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
68 views

Compute integral symbolically

I want to compute the following integral: ...
-1
votes
3answers
146 views

Computing integral over explicit region [closed]

I need to integrate $f(x,y)=y^2-2x^2y+6x^3-3xy+2y-6x$ over $\{y\geq 2x^2-2, y\leq 3x\}$ Im using Boole in the following way; ...
2
votes
2answers
209 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 = ...
2
votes
5answers
395 views

Compute Triple Integral on spherical coords

I need to compute: $\int \int \int z dxdydz$ over the domain: $\{x^2+y^2+z^2\leqslant 16,z\geqslant 0\}$ Im trying to use spherical coords as: $$\int_{0}^{2\pi} \int_{0}^{\frac{\pi}{2}} ...
0
votes
0answers
39 views

NIntegrate Issue: Changing integration limits makes calculation time extremely long

After a long time developing some code in mathematica and finally getting it to work, I have unfortunately encountered an odd problem: When I change the limits of integration (and shift the function ...
-3
votes
1answer
69 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
71 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 ...
1
vote
1answer
87 views

Write an expression as a full derivative

Is there a command that tells Mathematica to try to write the terms (if possible) of an expression as total derivates? Example: I want to tell mathematica to write ...
1
vote
1answer
91 views

How to obtain a useful answer from integration when Simplify is insufficient?

I have been trying to integrate a function AND get an output that is sufficiently simple as to be usable. Simply using the Simplify and ...
7
votes
3answers
513 views

Any way I can solve this integral?

So, Mathematica can't solve it. Any workaround? \begin{equation*} \int_0^\pi \frac{1}{\sin\left(\frac{\theta}{2}\right)^\beta + 1} \mathrm{d}\theta \end{equation*} The code is: ...
0
votes
1answer
90 views

Symbolic integral including Hermite polynomial does not evaluate

I am trying to evaluate the following integral: Integrate[HermiteH[n, Sqrt[a]* x] * Exp[- (c/2)* (x^2 + y^2) + b* x * y - (a * x^2)/2], {x, - Infinity, Infinity}] ...
0
votes
1answer
62 views

Definite Integral, Piecewise, Error

I am trying to evaluate the following: ...
0
votes
1answer
135 views

How to solve this integral equation?

I am trying to solve for x the integral equation : ...
3
votes
0answers
114 views

What can I do to improve the performance of my calculations?

I'm trying to express a simple probability problem in Mathematica, but am having trouble getting my calculations to execute at a reasonable speed. I have an object whose unknown location is modeled ...
0
votes
0answers
69 views

Multivariable Delay Diff. Equ. with Ndsolve and Nintegrate

I'm trying to simulate the following equation in Mathematica for $u(x,t)$: $$\frac{1}{\alpha} \frac{\partial u(x,t)}{\partial t} = -u + \int_{-\infty}^\infty {\rm d} y w(x-y) f(u(y,t - |y|/v))$$ ...
1
vote
1answer
95 views

Difficulty finding Expectation of a special function

I have a special function given as: $${\rm f}\left(r\right) ={1 \over \beta\lambda}\,2^{r/\beta} \exp\left({\left[2^{r/\beta} - 1\right]K \over \lambda}\right)$$ I should find the Expectation of ...
0
votes
0answers
84 views

Solving for a variable within a definite integral using FindRoot

I want to solve for P in this equation: Integrate[1/((P/(M*V)) - r*g - c*A*(V^2)*p/(2 M)), {V, 0, 26.82}] = s , where all constants are given except P. I've ...
3
votes
0answers
104 views

Non-linear integral equation

I'm trying to solve with Mathematica an integral equation. I found this excellent answer (How to solve a non-linear integral equation?) solving with a collocation method a problem which can be ...
0
votes
0answers
79 views

Exponential function Integral

I have tried to solve this integral: Integrate[E^(-((a^2 b c^2)/(a^2 + b)))/(a^2 + b)^2,a] Mathemathica is not able to solve it, I have tried the integration by ...
-3
votes
2answers
120 views

Find the value by using FindRoot command [closed]

The equation x^4-3 x^3 = cos(3x)+3 has two real solutions on the interval from -10 to 10. Lets call these two solutions r and s. Use Mathematica's FindRoot command to find r and s. Now let M equal the ...
4
votes
1answer
211 views

Using Boole to integrate over region

I have a complex and long piecewise function to integrate, so I have written a Mathematica script that cuts the whole range of integration, evaluates the integrand in each region and then integrates ...
0
votes
0answers
381 views

Solving a linear fourth-order fractional integro-differential equation

Definition: A real function $f(x)$, $x>0$ is said to be in space $C_\mu$, $\mu\in \Bbb R$ if there exists areal number $p$ ($>\mu$), such that $f(x)=x^pf_1(x)$, where $f_1(x)\in C[0,\infty]$, ...