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.
5,116
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Finding an increasing or decreasing function
I have a problem where I am given the derivative of a function, asked to graph it, then state where it is increasing or decreasing using Mathematica.
f'(x)=(x^2-3^x)/2x 0<x<4
I've tried the line ...
2
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2
answers
136
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Confused about the output of `CosIntegral`
I am interested in the properties of the cosine integral function, in this case the anti-derivative of Cos[Pi*x]/x, which Mathematica evaluates to ...
- 2,273
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Checking the sign value of the derivatives of a complicated function
Consider the following function:
...
- 765
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77
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Integration with respect to functions
I observe some strange behaviour of Mathematica when pulling functions into the integrator. I know that Mathematica's capabilities are limited when computing Stieltje or Lebesgue Integrals. But even ...
- 187
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How is the result of this integral obtained by the function `Integrate`?
When I use Mathematica to calculate
$$
\int_0^{+\infty } \frac{\log (1-\mathrm i x)}{1+x^2} \, \mathrm dx ,
$$
I get different results using functions NIntegrate ...
- 399
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Partial Derivative after Numerical Integration of a Complicated Expression with Singularity at Zero
I want to generate Fig no. 2,3,4 from https://arxiv.org/pdf/2212.08237
with the help of the following equations. In Fig 3 t_(opt) is the time Q_T reaches its max value Q_T(opt) for each T.
Here is ...
- 341
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56
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Why does Mathematica not find that integral depending on a parameter?
Integrate[(Log[1+a*x]/a)*Exp[-(Log[1+a*x]/a)^{2}]/1+a*x,{x,-Infinity,+Infinity}]
I don't know what I'm doing wrong. I've already done integrals similar to this one ...
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StreamPlot3d for the magnetic field of a loop
I am trying to go beyond StreamPlot in the case of a current loop that produces a magnetic field. My code works for StreamPlot, but does not end when I use the same field expressions with StreamPlot3D....
- 43
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Integration of the product of two exponential functions
How can I find the value of this integral?
Integrate[E^((-b)*t^a - k*t), {t, 0, Infinity}]
- 904
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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 ...
- 431
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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 ...
- 123
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365
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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 ...
- 27.2k
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7
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711
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Numerical approximation of the integral by using data
I want to use the numerical approximation of the integral of a function given a list of data:
$$\int_a^bf(x)dx\approx\sum_{k=1}^N\frac{f(x_{k})+f(x_{k-1})}{2}(x_{k}-x_{k-1}),$$
where $f(x_0)=f(a)$ and ...
- 685
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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 ...
- 421
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Checking the formula for solving the Poisson equation with an integral over all of space
EDIT: According to 2.2.3 Rigorous derivation, if we find the integral $u(x,y) = \int \int G(x,y,m,n)f(m,n) dm dn$ then we obtain a function that satisfies the Poisson equation $\nabla^2u(x,y)=f(x,y)$. ...
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