# Tagged Questions

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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### When evaluating this integral Mathematica returns two different answers

When evaluating this integral in Mathematica 10.3 Student Edition: ...
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### Evaluate a double integral over a region [duplicate]

How can I evaluate a double integral over a region in Mathematica? For example $\qquad \iint(x^4+y^2)\,dx\,dy$ for the bounded region $y=x^2$ and $y=x^3$
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### Non-rectilinear integration of InterpolatingFunction

Bug introduced in 7 or earlier and persisting through 10.3.1 [CASE:3487737] I have a 2-d array that I would like to resample into a different coordinate system and integrate along one of the new ...
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### Integrating sinc function over discontinuity

I would like to analytically integrate the sinc function. First of all, if I just perform the integration the following way, everything is as expected: ...
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### Triple/Double integral over outer side of a cylinder

$$\underset{S}{\iint} (yz\text{dx}\text{dy}+xy\text{dxdz}+xz\text{dydz})$$ Where S is the outer side of a part of a cylinder: $x^2+y^2 = r^2 ; x\le0,\ y\ge0, \ 0\le z\le H$ The problem about that ...
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### Two different results for same symbolic integral

I am trying to compute the following integral $\int_0^\infty dk \frac{e^{i k a}}{k^2}[\sin(kb)-kb\cos(kb)]$ When computing it as-is, i.e, with the code ...
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### Why the strange limit?

When we take the limit, we get an Interval. Why? What does it say about the function? I know that when $0$ or $\pi$ are substituted we get exact values, otherwise ...
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### How to show steps of Integrate[Exp[-(I*(s*t))]/(Sqrt[2*Pi]*Sqrt[s]), {s, 0, Infinity}]? [duplicate]

I am trying to use Wolfram Alpha in Mathematica 10.2 to show me the steps for calculating the integral in the title, i.e I have written the following command: show steps of ...
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### When is RegionMeasure[ImplicitRegion[…]] faster than (N)Integrate[Boole[…]]?

I wanted to use Mathematica to compute areas and volumes of various implicitly defined regions, so I ran a simple test case using the unit circle: ...
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### Integrate not restricting variable with Assumptions option?

I am integrating g over the region: ...
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### Integrate is giving finite result for divergent integral

Integrate[Exp[c x]/x, {x, -a, a}] returns ...
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### Integral Bounds and RegionPlot3D

We a tough problem in class today preparing for the final exam next Monday. $$\int_0^{\pi^{1/4}}\int_0^z\int_y^z 12y^2z^3\sin(x^4)\,dx\,dy\,dz$$ I was extremely surprised that I could simply type in ...
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### Integrating differential solid angle over the unit hemisphere

When reading about rendering topics I commonly run into integrals over a hemisphere similar to this one: $\int_\Omega n \cdot l \, d\omega$ If I want to put that in Mathematica then I can ...
102 views

### Solving this equation with NDSolve

I'm trying to solve a differential equation numerically. I've written this code but it is leading to some errors "initial history needs to be specified for all variables for delay-differential ...
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### Why i cannot get a numerical result? [closed]

I have tried following code: Limit[((sinx)^6)/(cosx - e^(-(x^(2))/2) + (x^(4))/12), x -> 0] Following is the image representing what I have tried to ...
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### Integrate dealing with Sqrt gives wrong answers

I often find when I integrate something with a Sqrt[x] term in it, Mathematica gives an incorrect result. I assume this must be due to some kind of incorrect ...
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### How to typeset and evaluate $u \big|_a^b$

Sometimes I need to evaluate an expression at the end points. e.g. the right hand side of $\int_a^bf(x)\textrm{d}x=F(x)\big|_a^b$. $F(x)$ could be complex at the right hand side so I can't just ...
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### Using Mathematica to find the areas described by polar curves

I am working on a project and I need to find the area of the surface inside the polar-curve $r=2\cos(\theta)$ and outside the polar-curve $r=1$. The graph is pretty straightforward: just two ...
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### Efficient calculation of leading order behavior of rational function under a limit?

Considering a rational function, as for example myExpr=(x+3)(2+5x+6x^2)/(x(x-5)(x+20)) I would like to have a function that tells me the leading order behavior ...
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### Derivative of piecewise function

I tried to find $f'(0)$ of this function: $$f(x) = \begin{cases} x\cdot\sin(\frac{1}{x}) & \text{if x\ne0} \\ 0 & \text{if x=0} \end{cases}$$ This is what I tried in Mathematica: ...
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### Evaluate Limit only if both directions(sides) are equal?Ex: $\lim _{x\to 0}\left(\frac{1}{x}\right)=DNE$

I want the limit of a function to only evaluate if both the left and right hand side are equal. For example $\lim _{x\to 0}\left(\frac{1}{x}\right)$ doesn't exist(two sided limit). However, the right ...
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### Plotting singular integral

I need to plot the following singular double integration $u(x,t)$ for $t=0, t=0.2, t=0.4, t=1$ and $t=2$ in one figure as a line. That is, I need $u$-coordinate vertically and $x$-coordinate ...
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### How to evaluate the limit of a function consists of Range

I would like to evaluate the limit: $$\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5+\cdots}}}}}$$ Therefore, I write the following function of n: ...
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### Defining arbitary Derivatives of functions

If I have two functions like these f[a_,b_] and g[a_,b_]. Lets say ...
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### Apply Grad and Mod to Matrix

Let f:=x^3+y*x*z+z^3; Let mat = {{2, 2, 2}, {3, 1, 7}, {1, 6, 3},{4, 5, 1},{0,4,9}}; be a list of points . I want to compute ...
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### How to fix internal error “too much recursion” when trying to compute a definite integral

I'm completely new to Mathematica. I got a 14 day free trial and I'm using the online version. I'm trying to use it to check the results of an integration I performed by hand. But I'm not getting any ...
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### How can I calculate the following integral?

I tried to calculate Integrate[(9.07 - 5.60 Cos[.87 t] - 2.71 I Sin[.87 t] + 2.14 Cos[1.74 t] + 2.70 I Sin[1.74 t] )^0.5, {t, 0, T}] but the output is the ...
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### Evaluation of this definite integral

I want to obtain the symbollic expression for this integral: $\int^\infty_{-\infty} \, dx \, \left(\frac{y - x}{R^2 + (y-x)^2}\right)\, e^{-\frac{(x - \mu)^2}{4 s^2} - \frac{i k (y - x)^2}{2 R}}$, ...
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### Infinite sum not evaluated unless split into even and odd terms

This sum s = Sum[Gamma[k/2]/(2 k!), {k, 1, ∞}] $\sum _{k=1}^{\infty } \frac{\Gamma \left(\frac{k}{2}\right)}{2 k!}$ is returned unevaluated (version 10.1.0). ...
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### Calculate overlap coefficient between two functions

I have two functions and I want to calculate the overlap coefficients between those two functions. A similar question has been answered for Python and R, however, I couldn't find an answer for ...
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### Adding more specific assumptions to Integrate

Let's say I would like to find a symbolic form for the integral $$\int_0^{2\pi}\sin^nx\,\mathrm{d}x$$with the added condition that $n$ is not only an integer, but an even one at that. Can this be ...
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### Integration of a piecewise function

Define f[x_, i_] := Piecewise[{{1/n, 0 < x < (i - 1)/n}, {(i/n - x), (i - 1)/n < x < i/n} , {0, i/n < x}} ]; I would like to compute ...
173 views

### Dealing with indicator functions

I am calculating the integral of two indicator functions with Mathematica. I'm having difficulty in imposing assumptions. What I have done so far: To define an indicator function: ...
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### Region bounded by x^2+y^2=1, y=z, x=0, z=0, in first octant

I need to draw (pencil and paper) the region bounded by $x^2+y^2=1$, $y=z$, $x=0$, and $z=0$ in the first octant. So the first assistance I asked of Mathematica is: ...
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### How to solve this definite integral in mathematica?

I am a beginner in mathematica. I tried to solve this integration but not able to solve it. Can any body help me how to solve this integral in mathematica? Here is my integral, \int_{a}^{b} ...