# Tagged Questions

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

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### Mismatch between numerical and analytic evaluation of an integral

I evaluated the following integral $$\int_0^1 \sqrt{r} \left | \cos \left(\left(k+\frac{1}{2}\right) \pi r\right)\right | dr$$ ...
330 views

### Solve ODE $d^2u/dx^2 + u/A = 0$

How can I solve following ODE with Mathematical: $$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$ with the conditions: $$\left.\frac{d^2u}{dx^2}\right|_{x=0} = 0,$$ $$u(x=0) = B$$ and ...
272 views

### Integrating a periodic function

I have a periodic function ff: ff := Function[x, Piecewise[{{ff[x - 1], x >= 1}, {2 x, 0 <= x < 1}, {ff[x + 1], x < 0}}]] Plotting it works fine: ...
152 views

### Integral with unreliable result

I want to calculate $\int_R^1 \sqrt{r} |\cos((k+\frac{1}{2})\pi r)|dr$ and I get a result from Mathematica. Then I try to check the result putting the value of $k$ and $R$, (k=1 and R=0.5) in the ...
119 views

### a mysterious error in multiple symbolical integration

I am trying to do the following integration: ...
346 views

### Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
186 views

### Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
93 views

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

The following: ...
240 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 ...
338 views

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

Mathematica can't find a solution to this Expectation. ...
106 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 ...
87 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 ...
232 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 ...
794 views

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### Second derivative implicit differentiation using Wolfram Alpha input?

How would you perform second derivative implicit differentiation using Wolfram Alpha input? The reason that I'm using WA input is that it gives you step-by-step solutions and I'm a first year ...
110 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 ...
138 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 ...
1k 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 ...
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: ...