# Questions tagged [calculus-and-analysis]

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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### Is there a more efficient way to calculate the variance of a random variable given two sets of data?

Given two lists, one being the values of a random variable and the other being their corresponding probabilities, how can we calculate the variance of the random variable? ...
189 views

### How to calculate this improper integral?

How to calculate the Integral involving MarcumQ function whose Integral interval is (0, +Infinity)? Any help (code or reference) would be greatly appreciated. ...
1 vote
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### Incorrect limit involving hyperbolic Kepler equations

I’m trying to work with the Kepler equations for a hyperbolic trajectory in the case of a repulsive force (see Wikipedia for the attractive case). The trajectory can be described by the right branch ...
43 views

### Contour integral around a circle centred just off the origin [closed]

In the documentation, a Basic Example of ContourIntegrate is given as $1/z$ integrated along the unit circle: ContourIntegrate[1/z, z \[Element] Circle[]] which ...
128 views

250 views

### Integration involving Piecewise function and DiracDelta function

I want to calculate an integration, which reads where $\delta\left(q_{23}^{01}\right)=\delta\left(1+q_1-q_2-q_3\right)$ and $\mathrm{min}(1,q_1,q_2,q_3)$ means the minimum of $(1,q_1,q_2,q_3)$. What ...
370 views

### Possible bug in partial derivative [closed]

In 14.0 on Windows 10 let us consider D[Min[x, y], x] Piecewise[{{1, x - y <= 0}}, 0] As I understand it, the result is ...
44 views

### Integrate diverges for convergent integral, and returns unnecessary condition

I'm trying to solve an infinite integral using Mathematica. For some reason, Mathematica claims the integral diverges although when solving to a finite limit L and ...
1 vote
330 views

### Slope of a line

Just a quick question. Is there a fast inbuilt function to calculate the slope of a line segment passing through two points {p11,p12} and ...
### Describing the region of integration $\mathbb{R}_+^n$ for arbitrary $n$
Let $f_n:\mathbb{R}^n \to \mathbb{R}$. I would like to know an elegant way of writing the integral $$I_n = \int_{\mathbb{R}^n_+} f_n(x)~\mathrm{d}x$$ in Mathematica. For fixed $n$, the best I could ...
The present question is pretty similar to this one. Here I want to find the solution of the following implicit integral equation:  P_H(u)=\int_{-\infty}^\infty dJ \int_{-\infty}^\infty du_1 \int_{-\...