# 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.

2,735 questions
Filter by
Sorted by
Tagged with
0answers
41 views

### Find inverse of a complicated function

I am looking for an analytic inverse function for ...
2answers
99 views

### Unexpected limit result (was: How to fix the limit problem?)

MATHEMATICA fails in proving that Limit[ Integrate[ x^(x - 1) , {x, t, 2*t} ] , t -> 0 , Direction -> "FromAbove" ] == Log How to fix ...
1answer
38 views

### Plotting cylinders and planes on the same graph

How would I plot the cylinder $y^2 + z^2 = 9$ and the planes $x = 0$, $y = 3x$, and $z = 0$ in the same graph and in the first octant. ...
1answer
35 views

### How to graph a solid

Given a solid described by $S = \{(x,y,z)|0\le x\le4-y^2, -2\le y\le2, 0\le z\le y+2\}$, how do I graph the solid? I have already tried a RegionPlot3D but I might ...
0answers
65 views

1answer
49 views

### How to solve this equation by Solve?

I have an equation to be solved. But Mathematica does not work for it. I hope the solution x can be expressed as a function of a and b ...
1answer
37 views

### how can I plot two variables (inside a definite integral) against each other

I want to plot x against y in this relation:
1answer
28 views

### How to mark non-pre-defined functions as functions of a certain variable during calculation of derivative?

If I have some calculation $X=v\cdot\delta$ and I want to calculate $\frac{\partial}{\partial v}X$, the result according to Mathematica is $\delta$. Now, I want to define $\delta$ as a function of $v$ ...
0answers
32 views

### Why do I get the error message as integral does not converge?

Can anyone please help me to find the integral value of the following expression, Integrate[(x - t)^(-1), {t, 0, x}] It will be of a big help to me.
1answer
72 views

### Evaluating an integral combining a Bessel function with some other functions [closed]

How can I evaluate the integral of $j_1 ^2(x)\exp(-bx)/x$ from 0 to ∞?
1answer
73 views

### Variable dimensional integrals

I need to Integrate a function, but let the number of dimensions vary. Integrate[Product[Exp[-( t[[i]] )^2], {i,1,4}], options] ...
2answers
103 views

### Evaluating FourierTransform like integral manually

I am trying to evaluate Integrate[x^2*Exp[I k (x - 1)], {k, -∞, ∞}, {x, -∞, ∞}] Since $\frac{1}{2\pi}\int_{-\infty}^{\infty} e^{ik(x-1)} d{k}$ is $\delta(x-1)$, ...
1answer
36 views

### Limit of an integral and hypergeometric function

I want to evaluate the following integral: Integrate[Sin[θ]^(D1 - Nc - 1)/(A Cos[θ] - I ϵ)^(N1 - Nc), {θ, 0, π}, Assumptions -> A > 0 && ϵ > 0] ...
2answers
138 views

### Compute unstable integral with high precision

I want to calculate $$\int_{\mathbb{R}^n} e^{-t_1^4-t_2^4- ...-t_n^4-(1-t_1-t_2-...-t_n)^4} \text{d}t_1 \text{d}t_2 ... \text{d}t_n$$ with the highest possible n. I tried with ...
4answers
442 views

### How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$?

How can I simplify $\lim_{n\to \infty } \, \int_0^n e^{-x} \left(1-\frac{x}{n}\right)^n \, dx$ ? Limit[Integrate[(1 - x/n)^n/E^x, {x, 0, n}], n -> Infinity] ...
3answers
492 views

### How do I find and plot the intersection of these three surfaces?

I know how to find the region of intersection of these cylinders using integration, but how would I plot that in mathematica? This is what I have ...
1answer
82 views

### Problem in Integration

I want to calculate both of these integrals: Integrate[1/Sqrt[c x + Sqrt[ b x + x^2] + a], x] and ...
1answer
93 views

### Calculation of sum \begin{aligned}\sum_{k = 1}^{n - 1}\end{aligned}\left(1+\cos\left(\frac{k\,\pi}{n}\right)\right)^n

Having established that Mathematica cannot calculate the following summation: sum = Sum[(1 + Cos[k Pi/n])^n, {k, 1, n - 1}] I implemented the classic "plan B", ...
1answer
88 views

### When to trust Integrate?

I'm trying to get an analytical expression for the following integral: ...
2answers
167 views

### On Certain Characteristic Function

I am trying to find the characteristic function for Johnson's SU distribution by integrating the probability density function with Exp[I*t*x] but Mathematica is ...
1answer
60 views

### Is there any way to do this integral without expanding the exponential power?

Integrate[ x^(1/2) Exp[-10.7* c/x] Sqrt[(1 - (125/1000)^2) (1 - (2*4.18/125)^2) - (1 - (2 x/ 1000))^2], {x, 5.03, 994.97}] or can i do this indefinite ...
3answers
108 views

### Problem with minimization of $x^z$

I have plugged in the following problem Minimize[{x^z, z >= 1, z <= 10, x >= 1}, {x, z}] Can anyone explain please why the software does not provide the ...
1answer
38 views

### How to deal with the derivative of an variable upper limit integration by the symbolic form?

I need a rusult with the following form D[Integrate[f[t], {t, low[x], upper[x]}], x] (*Out[]=-f[low[x]] (low^\[Prime])[x]+f[upper[x]] (upper^\[Prime])[x]*) My ...
1answer
36 views

### Interesting output in Integrate [closed]

I found interesting behaviour, best illustrated in the following example. When trying to evaluate Integrate[1/(d^2 - 1), d] Mathematica 11.3 gives the following ...
0answers
44 views

### Fitting a Curie-Weiss law function with a diverging point to a data

I would like to fit a function to some experimental data such that the extracted value of Curie temperature (Tc) describes the temperature at which the response flattens out to a constant value. ...
0answers
23 views

### Problem with integrating special function under assumption

i found different results when integrating a special function (see below), depending where i place my assumption (x > 0, x0 > 0). The problem is that the two solutions are not compatible. In fact, if ...
1answer
64 views

### Integrate a function of NDSolve

I'm having this problem of integrating a function that's the solution of a NDSolve multiplied by another function. I basically compute a cycle wich add at each step the quantity ...
1answer
55 views

1answer
63 views

### NIntegrate a singular function

I am trying to do this integral numerically: ...
0answers
22 views

### Assign a Derivate to a new fuction variable

I'm having a new problem. I'm trying to create a new function from a Derivate of another function, but i'm can't getting it. Someone could help me? I'm thinking that is something in the syntax of the ...
1answer
63 views

### How to find the maximum of a function with several variables symbolically?

I want to maximize a function with respect to tau1, tau2, and alpha, and it is like the following: V + β1 τ1 - α τ1^2 - β2 τ1^2 + \τ2 - 2 τ2^2 + α τ2^2 I know I ...