# Tagged Questions

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

61 views

### Functional in Integration [closed]

I have evaluated the following code: k[θ_] := Sin[θ/2]^2; Do[Print[Integrate[1/Sqrt[1 - k[θ]*(Sin^2)[ϕ]], {ϕ, 0, π/2}]], {θ, 0, π/3, π/12}] But I don't know why ...
154 views

### How to integrate a function of a direction, over the hemisphere

The Mathematica documentation Integrate over Regions gives an example of how to simply integrate over a sphere (surface): ...
46 views

### Solving Integral -syntax or interpretation problems

WA interpreter achievement not well this entry from Mathematica, steps need to see the full resolution input WA ...
143 views

### Evaluating two equivalent integrals apparently gives two different results

I have a integral and I use two different symbols in an interchangeable way, but I do not get same expressions when I swap them. Can some one explain why? ...
104 views

### Strange kernel segmentation fault in Integrate

Bug introduced in 8.0 or earlier and persisting through 10.4 Define tointegrate = D[V[y1[t], y2[t]], y2[t]] D[V[y1[t], y2[t]], {y1[t], 2}] and try to find its ...
110 views

### Is it possible to double integrate my function over real numbers?

I have a fairly complicated function: ...
122 views

### Calculate an integration limit to obtain a certain area under a curve

I have a function that looks like a sigmoid curve. I would like to calculate the right integration limit so that the area under the sigmoid curve has a given value. my curve: ...
159 views

### Piecewise Integration

I am trying to integrate a piecewise defined function twice. It represents the acceleration of a projectile. I am obtaining it's position as a function of time if it starts from rest at the ground, ...
240 views

### Limit of partial sums involving inverse squares

Consider the finite sum rs[x_, n_] := x/n Sum[n^2/(i + (n - i) x)^2, {i, 1, n}] Is there a way to bring Mathematica to calculate the limit for ...
223 views

### Is it a bug in Limit?

Bug introduced in 9.0 and fixed in 10.0.0 Mathematica 9 on Windows and WolframAlpha says Limit[Sin[Sqrt[x+1]]-Sin[Sqrt[x]],x->Infinity] is Interval[{-2,2}]....
96 views

### Symbolic Integration gives wrong answer [closed]

I have tried to integrate the following expression in Mathematica 10.1 ...
149 views

### Express function derivative in terms of the function itself

I'm working on a minimization problem that involves the standard logistic function $f(x) = \frac{1}{1+e^{-x}}$ along with its simple derivative $f'(x) = f(x) \cdot (1 - f(x))$ The correctness of ...
190 views

### Finding extremums of Abs[complex function]

We have a function same as f[x_]=Cos[x] Cos[2 x] + I Sin[x] Sin[2 x] The final objective is to find all extremums of Abs[f[x]] in [0,2 pi]. But in the first ...
362 views

### Limit of a real function

Evaluating Limit[2^x Log[x], x -> 0, Direction -> -1] (right limit) gives correctly the answer -∞ but the ...
73 views

### Differentiate functions

I have two functions: F1[t_, g_] := a1*t + a2*g F2[t_, g_] := b1*t + b2*g I want to evaluate $(dt/dF1)_{F2}$; i.e., differentiate $t$ over $F1$ when $F2$ is ...
179 views

### Implicit function theorem to higher order

Consider f[x_, y_] := Csc[0.482 y] Sin[0.963 x - 0.482 y] + 3.247 Csc[0.333 y] Sin[0.667 x - 0.333 y] + 5.049 Csc[0.119 y] Sin[0.238 x - 0.119 y] I'...
60 views

### Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
207 views

### Slightly increasing complexity of function increases calculation time by magnitudes

I am trying to calculate an impedance value from voltage and current functions. The calculation method is based on how an actual measurement device performs it. I have two different current function, ...
142 views

### Differentiate a numerically defined function

My function is f[a_, b_] := NIntegrate[Sqrt[(Cos[t] - a)^2 + b^2], {t, 0, Pi}] I want to calculate g[1,1] where ...
226 views

### How to make Mathematica express an equation in terms of previously defined functions

I was given a problem for my physics class, and perhaps I have taken it too far, but I wish to finish what I started. I have a function (i warn you that this does not look pretty) ...
271 views

### Residue theorem and multiple poles in contour integral

I had a query on multiples poles in [Contour Integral][1] using the [Residue Theorem][2]. I had an integral which I wanted to solve using the Residue Theorem. By the help of mathematica experts i ...
119 views

### How to express and take symbolic derivative of expression with finite sum

I have the expression: $$p_i = \frac{e^{x_i}}{\sum_{j=1}^{n} e^{x_j}}$$ which I defined with the following Mathematica code: ...