# Tagged Questions

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

266 views

### Integral converging in M9 but not in M10

Background: Mac OSX 10.9.4, Mathematica 9.0.1 vs. Mathematica 10.0 (both versions are Student Editions). I have a notebook. It used to evaluate fine in Mathematica 9. I upgraded to 10 and, without ...
97 views

### Result of symbolic integration changed drastically by making assumptions

I would like to know the underlying reason for different outcomes for the two integration operation below. One of them includes a few assumptions, otherwise both have the same integrand: ...
51 views

### Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as ...
140 views

### Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
46 views

### Evaluation of integral [closed]

I want to evaluate an indefinite integral using the Integrate command, and I know that the answer can be written in terms of elementary functions (square roots, logs etc.) but Mathematica seems to ...
92 views

### Convoluting inverse square root with Gaussian

I would like to convolute the inverse square root on the interval [0,inf] with a Gaussian function, like so: ...
71 views

### Integral calculation in Mathematica [closed]

I need to calculate this integral using Mathematica: ∫ t^z * ln(t) dt from x to y with the assumptions that z is an integer and 0 < x < y This is what I'm trying to do: ...
66 views

### Symbolic integration of elliptic functions

Is there some clever way to integrate products of elliptic functions $\wp(z;g_2,g_3)$ or $\zeta(z;g_2,g_3)$ in Mathematica? Mathematica seems to be able to integrate functions like ...
257 views

### Generating a polynomial that's accurate to within an error of no more than 1/10^5

I'm currently stuck on a question for class that asks... "Find a polynomial p[x] that you can use to calculate 6 ArcTan[x] to ...
103 views

84 views

### Result of Integrate depends on order of integration although the domain is rectangular

The following: ...
125 views

### Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
261 views

### Conditional Expectation — How can Mathematica find a more general closed form?

Mathematica can't find a solution to this Expectation. ...
93 views

### Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...
174 views

### Mathematica policy for correctness of results [closed]

Does Mathematica provide any kind of warranty that their calculations are correct? Say I'm running a billion dollar company, and I relied on Mathematica to do calculations, like aerodynamics or car ...
79 views

### A problem with “RiccatiSolve::ncsol: Cannot compute a stabilizing solution to the matrix equation ”

I have a SSM ( State Space Model ) and I want to calculate its optimum gains unisng LQOutputRegulatorGains[] command. When I run the code, it solves the equations ...
107 views

### Integral over geometric region [duplicate]

I'd like to calculate this integral $$\int_E y\ dydz$$ where $E = \{ (x,y,z) \in R^3 : z^2+6 < y^2 < 5z \}$ By hand i've got $\frac{1}{12}$ but i'm not sure, and i'd like to verify this ...
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; ...
94 views

### Complex Convolution

I am attempting to integrate a convolution variable using the following code. However, the program is taking too long to complete the integration. Does anybody have any coding tips that may make ...
85 views

### Defining a function that differentiates another function with rule replacement

This question is related to the question I posted here. In that question, I thought I have simplified my original problem into an equivalent concise version, but I found that it is not. So I decided ...
128 views

### Finding the maximum of a gradient vector

Im trying to find the maximum of my gradient vector G[x,y], I've tried several options including FindMaximumValue, FindMaximum etc. but i couldn't find it. The full function is shown below, any help ...
131 views

### Plotting a multivariable function [closed]

m[x_, y_] := 0.9*Exp[-((x - 1)^2 + (y - 1)^2)] + 0.5 Exp[-(3^2 ((x - 2.5)^2 + (y - 1.5)^2))] I'm trying to create a 3d plot for the function above. I tried ...
65 views

### Forcing an integral to be solved in separate terms

Using Mathematica I want to solve an integral over a function that contains both determined and undetermined parts which looks like this: ...
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 $E[Y] = \int_0^\infty y f_Y \ dy = ... 1answer 205 views ### Gateaux (directional) derivatives and higher order differentials of a functional I would like to calculate the Gateaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional:$L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$... 1answer 115 views ### Generate conditions seems to not work [closed] I am trying to compute the following integral Integrate[E^(I*k*Omega*t), {t,0,T}, GenerateConditions->True] for which Mathematica returns ... 1answer 91 views ### Integrate and NIntegrate yield different results for double integral Evaluating a double integral with bivariate normal distribution yileds widely different results depending on the method used. I define a bivariate normal distribution with {10, 3} and {8, 1.5} as ... 3answers 166 views ### Answer when integrating by partial fractions Evaluating $$\int \frac{x^2-x+5}{(x-2) (x-1) (x+3)} \, dx$$ Version 9.0.1 gives the following answer $$\frac{1}{4} (-5) \log (1-x)+\frac{7}{5} \log (2-x)+\frac{17}{20} \log (x+3)$$ It seems to ... 2answers 232 views ### Function given exact arguments returns hugely different value than it returns when given equivalent inexact arguments I was trying to compute the probability that a coin is from a particular underlying distribution given that a particular set of tosses was observed. (I know this can be done in a different way, but I ... 1answer 101 views ### Using Mathematica to find Derivatives I am given a system first order differential equations:$x'=y$and$y'=6x^2-a/2$, where$a$is a constant and$'$denotes$t$-derivatives. I then make the substitution$(x,y)=(x_1y_1,y_1)$. This ... 5answers 120 views ### Using Mathematica to find a Derivative I am given a system first order differential equations:$x'=y$and$y'=6x^2-a/2$, where$a$is a constant and$'$denotes$t$-derivatives. I then make the substitution$(x,y)=(x_1y_1,y_1)$. This ... 8answers 957 views ### Finding maximum or minimum of implicit functions is there any built in function that can be used to find maximum or minimum of implicit functions? For example, if we have the equation $$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$ then we can visualize the ... 0answers 30 views ### How to calculate this derivative? [duplicate] Can Mathematica do the following simple calculation? $$F(x_0, x_1, x_2, ...) \equiv \sum_n x_n^2$$ I want to do the symbolic calculation: $$\frac{\partial F}{\partial x_m} = \sum_n 2 x_n ... 1answer 73 views ### Integrating a function forcing parameters to be real and positive I'd like to integrate the function f(x)=x^{a-1}e^{-b x} over the interval [0,\infty). f[x_] := x^(a - 1)*Exp[-b*x] Then: ... 0answers 58 views ### Computing integrals with differential operator I've to compute this expression$$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ... 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 = ... 1answer 67 views ### Integrating function can't be epressed? [closed] Hi I have a function in a form of $$\frac{a}{x}exp(\frac{b}{\sqrt{3}-x})$$ The code is Integrate[a/x*E^(b/(3^0.5 - x)), {x, 1, 3^0.5}] But it can't work ... 0answers 62 views ### A regularized hypergeometric function related question I'm interested in finding a way (if possible) of expressing this specific value of the regularized hypergeometric function in terms of known constants. How might I use Mathematica to check this ... 3answers 289 views ### Marking specific points on a 3D curve Here is the curve below. (written as a position vector) r = {Cos[7 Pi*t], Cos[6.2*Pi*t], 2.5*t} ParametricPlot3D[r, {t, 0, 2}] I want to know how I can mark ... 1answer 203 views ### Is this function convex? How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters$a,\,b$belonging to the interval$(0,1)\$ in ...
Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...