# Tagged Questions

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

820 views

### Can Mathematica tell me if a polynomial has all real roots?

I am trying on this polynomial, ...
127 views

### Continuity of function-example

I'd like to examine the continuity of the following function: f[x_] := Limit[(n^x - n^(-x) ) / (n^x + n^(-x) ), n -> Infinity] I know that this function isn't ...
224 views

### Curious solutions of x' = Sqrt(x), x(0)=4

Consider the solution of $x'=\sqrt{x}$, $x(0)=4$ using DSolve. ...
95 views

### Integrate gives Simplify::infd “simplified to Indeterminate” message

Using version 10.1 on windows 7 Integrate gives this Simplify::infd Kernel message. What causes it, is this a bug? ...
103 views

### Plotting a function based of a complicated integral

I would like to have help in making a plot of a complicated function based a definite integral. - desired graph My calculation: ...
117 views

### DiracDelta and version 10.0.0 [duplicate]

Note: This issue seems to affect version 10.0.0 only and is fixed in 10.0.1, 10.0.2, 10.1 and 10.2 When evaluating the following two inputs: ...
68 views

### Is there a way for me to get Mathematica show its steps? [duplicate]

I have seen similar questions but they were quite dated (3+ years). When performing, say an Integration, it would be beneficial to see the major steps such as variable substitution, change the order ...
74 views

### Using Assumptions in Expressions that Evaluate to be Elliptic Integrals

I have the following integral that I am trying to evaluate in Mathematica: $\int \sqrt{\alpha + m g l \cos(q)} dq$. If $\alpha > m g l$, then the result is a complete elliptic integral of the ...
176 views

### Revolution of two curves around the y-axis

I've looked through the other posts on rotating a function around the x or y axis and haven't had any luck. my question is this how do i rotate the area between the functions $f(x)=x^2+1$, and ...
623 views

### How can I obtain an asymptotic integral expansion at infinity?

I want to find the asymptotic expansion at $x \to \infty$ of the following function: $$I(x) \equiv \int_0^{\pi/2} e^{-xt^3 \cos(t)} dt.$$ To do this I defined ...
121 views

### How to compute DSolve or NDSolve for kind of piece wise function?

I need to Compute the expression for two functions. q[t] and q1[t] over certain range of time. The code is given below. ...
101 views

### Second derivative of SmoothKernelDistribution PDF?

Does anyone know why I can't seem to get a second derivative of this interpolating function f? In this example, h[x] is zero ...
121 views

### Computing a Gamma function-Gaussian integral

I would like to compute the following function: Integrate[Gamma[k,0,Exp[-2 e x^2]],x] k is an integer and ...
293 views

### How do I find the area between two polar curves?

More specifically above r=6 and below r=4+4cos(θ) graph of the two curves PolarPlot[{6, 4 + 4 Cos[t]}, {t, 0, 2 Pi}]
236 views

### Double improper integral

I am trying to compute the following double integral: Integrate[(r BesselJ[0, r])/( 2 (r^2 + z^2)^(1/2)), {z, -Infinity, Infinity}, {r, 0, Infinity}] Which ...
430 views

### Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
64 views

### Multiplying two sets of data (x,y values, but different x density) followed by integration of the product

I've been trying to do this by myself today, but no luck yet. Please, see attached image. Basically, I do have two data sets A (x1,y1) and ...
80 views

### Multiple Integral of equation including dx prime? [closed]

I'm hoping someone can verify I've written this function properly since I'm a little new to Mathematica. What I'm attempting to do is code a function that describes a gravitational field of an ...
331 views

### Integrate fails for generic parameters but works for any specific values (v. 10.0.x bug)

Bug introduced in 9.0 and fixed in 10.1 I was trying to get the following integral ...
127 views

### Limit of a sum as number of terms approaches ∞

Is it possible to find the limiting value of function at large N? ...
523 views

### Integrating a function over a surface integral

From a first principles bandstructure calculation I get an energy scalar field in three dimensions $E(x,y,z)$. It's now easy to plot a constant energy (contour)-surface for dedicated values ...
158 views

### Strange results from evaluating a simple integral

I am trying to do a seemingly simple integral in Mathematica 10 and am getting strange results: ...
279 views

### Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
133 views

### Imaginary terms in the derivative of Jacobi theta function (2) on the real line

I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$. Calculating or plotting the function itself works fine: ...
99 views

### How do I numerically integrate over a data set that has uncertainties? [closed]

I have a 1D data set {xi, yi} with no uncertainties in xi and with uncertainties dyi in yi. The resulting discrete function is monotonic and relatively smooth and I would like to integrate the ...
61 views

### Integrating expressions with several terms and delta functions

So I want to integrate an expression that looks something like this: Integrate[f[x]+DiracDelta[x-y]g[x],{x,-Infinity,Infinity}] With some more terms added with ...
94 views

### Forcing Exact Outputs for Integrate [closed]

I'm trying to compute the following triple integral: ...
115 views

### Partial derivative of defined function with vector input

Background: Have written a formula for the refractive index for a glass slab (n) that depends on the variables t,a and d. Now I want to calculate for example some sort of error and I'll be needing to ...
64 views

### Boundary condition not correctly imposed for NDSolve

I notice that when plotting the below NDSolveValue ...
89 views

### an Integral that should be doable:

Integrate[Cos[\[Beta]] Exp[I z Cos[\[Beta] - \[Alpha]]], {\[Beta], 0, 2 \[Pi]},Assumptions -> z \[Element] Reals] correct answer is [ I think ]: ...
260 views

### Why don't products of Dirac deltas integrate correctly?

Bug introduced in 10.0.0 and fixed in 10.0.1 The integral $\int \int \ \delta(x) \delta(y) \ dx dy=1$ evaluates to 0 in Mathematica ...
106 views

179 views

I want to find min of the function $$\frac{1}{\sqrt{2 x^2+\left(3+\sqrt{3}\right) x+3}}+\frac{1}{\sqrt{2 x^2+\left(3-\sqrt{3}\right) x+3}}+\sqrt{\frac{1}{3} \left(2 x^2+2 ... 1answer 82 views ### Four integrals, how can I expedite the calculations? I have to calculate the following multiple integrals (4 integrals) ... 2answers 388 views ### How can I get the inverse of my function? The original function is$$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$I want to express e^{\frac{\phi }{k t}} about m and f, so I tried: ... 1answer 210 views ### PDE of real-world system, integral boundary condition I've stripped all the physical-significance for clarity, but I know that u[x,t] will be everywhere positive and continuous. here are the equations in Mathematica code: ... 0answers 109 views ### How can I verify double integral solution? I have a double integral as follows 1-(\int_0^\infty (\frac{Cje\cdot Cte \cdot e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)^2} + \frac{e^{\frac{-w}{Cte}}}{(Cte+Cje \cdot w)}) ... 1answer 140 views ### How can I simplify a triple integral with exponentials? I want to simplify the following triple integral with exponential terms. \int_0^\infty\int_0^\infty \int_0^\infty \frac{1}{R\,G} e^{-p(1+R\,a)-q\, b \frac{1+R\, a}{1+G\, x}}\, ... 1answer 483 views ### Lagrange Multiplier We are asked to maximize and minimize f(x,y)=4xy, given the constraint 4x^2+y^2=8, using the Lagrange Multiplier method. First, I enter the functions f and g. ... 2answers 141 views ### Well-defined symbolic integral leading to ConditionalExpression I would like to determine a closed-form expression for the following symbolic integral$$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
I know that I can do, say, a triple integral such as $$\int_{a_x}^{b_x}\int_{a_y}^{b_y}\int_{a_z}^{b_z}f(x,y,z)\,dz\,dy\,dx$$ with the input ...
I'm trying to use Mathematica to compute a limit, because I have no idea how to compute it by myself. The limit should be: $$\lim _{n\rightarrow \infty }\dfrac {2^{n+1}-n-2}{2^{n}}$$ Any ideas?