# 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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### Plotting, Integrating two variable function with cross-restricted domain

Hello, I have two problems. the first is plotting 3D function, the domain is "0<x<y<1". (I could find examples like integrating function with domain 0<x<1, 0<y<1, but I ...
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1 vote
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### Integral of orthogonal Bessel functions

This is the basic form of the problem i am solving. The main difference with the integral on the photo and my example is that i have my integral defined from b to c instead of 0 to a, and Bessel ...
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### Integral with triangular functions in exponential and numerator

I am trying to find the solution of an integral with a triangular function in the numerator and in an exponential, but after an hour Mathematica has not given me an answer. I wondered if there is a ...
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50 views

### Useless and incorrect result of AsymptoticIntegrate

In version 13 on Windows 10 I try to find asymptotic of the integral used in potential theory ...
• 16.7k
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### Output of expressions unable to have operations be performed on the expression

I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as n := 4 ...
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### Plot for DSolve in mathematica [closed]

I don't Plot it's not working!!, can you help me? ...
49 views

### Integration over an implicit region

A question asks me to calculate the following integral using NIntegrate: Calculate the double integral ... where D is the area bounded by the four lines ... With ...
1k views

### Mathematica 13.0 simplifies trigonometric integral wrong

I calculate the following general expression: ...
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### Getting a wrong plot after NIntegration

I am trying to plot this function numerically. R2T = ...
1 vote
29 views

### Getting the same result from Integrate as Probability

I'm trying to solve a Baysian inference problem (although the details are not all that important for this question) I define two probability distributions P and <...
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### Numerical Plot for an example

I would like to compare the numerical and analytical solution with plot for this example but something is wrong I don't know how to fix it?!! ...
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1 vote
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### What's the meaning of Global?

I'm calculating an integral, Integrate[(t e^(-z t) e^(-q t))/(1-e^(-t)), t], and the result is ...
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### Settings that integrate gives also distributions as solutions

How can I tell Mathematica that I also want distributions as solutions for Integrate? Example: $$\int_{\mathbb{R}} \mathrm{e}^{\mathrm{i}kx}\mathrm{d}x=2\pi\delta(x)$$
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### Replace Derivative[ i ][ f ][ t ] with f[ i, t]

Assume the PadeApproximant is carried over f[t0] * g[t0] with the order {1, 1}, that is <...
101 views

### Integrate: slow and wrong results

Very often I struggle to understand what is happening when I try to integrate stuff in Mathematica. Generally, it deals very well with ugly symbolic integrals. But I have an example in which it deals ...
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### Incorrect result of AsymptoticSum

Trying in version 13 on Windows 10 ...
• 16.7k
57 views

### DSolve doesn't solve a second order differential equation

I am trying to solve an ordinary differential equation: ...
2k views

### Can Mathematica calculate this elliptic, triple integral?

Integrate[(4 a b/Pi) (a^2 + b^2 - 2 a b Cos[c])^(1/2), {a, 0, 1}, {b, 0, 1}, {c, 0, Pi}] I'm using basic plan, it gives me the result like that. The ...
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68 views

### Taking sentences with a spatial factor [closed]

To ask my question precisely, I should say that I have got many terms, among them some have coefficients $M^n$. Some things like : $$f = f_1(M) + f_2(M) + M f_3(M)+ M^2 f_4(M)+f_5(M)+...$$. I need to ...
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### How come I can't get $\int f(t)$ from performing derivative/anti-derivative operation on $\int f(t)$?

I know the the area under the curve of some function between the coordinates $t_0$ and $t_1$, is: $$\int_{t_0}^{t_1} f(t) \space dt=\frac{\left(t_0^2+t_1^2\right)^2}{4t_1^2}$$ How do I find $f(t)$? I ...
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### Selecting a solution range that is independent of a variable value

This symbolic computational question derives from this mathematical one on math.SE: Find all values of $a \in \mathbb{R}$ for which $f(x;a) = x^3 - 3 a x^2 + 3 a x - 2$ is non-decreasing. My ...
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118 views

### How to integrate this product of Exp[] and Cos[] using Mathematica

I would like to integrate the following product of Exp and Cos： ...
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109 views

### Evaluating PlusMinus to 2 decimal answers

How do I evaluate and expand an expression containing PlusMinus such that: N[PlusMinus[1, 1]] returns 2, 0 I'm stuck at ...
43 views

### Why does Mathematica not know some integrals diverge?

I want to analyse the convergence of some complicated 1d integrals that may have divergences at $x=0$, similarly to the harmonic integral $\int_0^a 1/x \ \mathbb{d} x$, which I know is divergent. When ...
36 views

### Assuming combined with mathematical notation of Integrate

I am trying to write down the following expression Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0] using mathematical ...
68 views

### The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
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### splitting integrand based on variable dependence

For multiple integration, I would like to automatically check whether the integrand can be split up to a product of terms, each dependent on as small a subset of the variables as possible. E.g., given ...
33 views

### Integer parameter assumption gives incorrect result when integrating

There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following: ...
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45 views

1 vote
69 views

### How do we just have $\log$ solution?

Mathematica solves this but I want the solution just as Ln[..]?!! DSolve[y'[t] == 3/2 a*y[t] ((y[t] + b)^2 - f), y[t], t] thanks
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### Power Series and Interval of Convergence [closed]

How could I find the power series and interval of convergence for x/(3+x^2)?
243 views

### Computing the elliptic integral $\int \frac{1}{x \sqrt{f+\frac{a}{x^3}-\frac{k}{x^2}}} \, dx$

I don't know how to solve this with or without Rubi?!! ...
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28 views

### Evaluating partial derivative at a point

I have a function in 5 variables, lkl, and I want to evaluate its second derivative wrt tau at a point. (I will also later want ...
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