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# 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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### Why does Mathematica miss some solutions for my integral?

When computing the integral of two orthogonal sine functions $\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0 Mathematica seems to miss the solution where $n=m$. I don't ...
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### NIntegrate a Triple Integral… Different Integration Strategies

I'm trying to evaluate a triple integral using NIntegrate. It takes the form: \begin{align} \int_{\omega_0-5\delta}^{\omega_0+5\delta} \mathrm{d}\omega \int_{\omega_0-5\delta}^{\omega_0+5\delta}\...
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### Singularity or stiff system in NDSolve

I have the following piece of code ...
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### Got MeasureDump when integrate over region with decimal parameters?

I had this problem when using Integrate over regions: ...
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### How to evaluate derivative for implicit

If $x = \frac{1}{2}y(y^2-3)$, how do I use Mathematica to evaluate $\frac{\text{d}y}{\text{d}x}$ at the point where $y=0$? Doing f[y_] = 1/2*y*(y^2 - 3) and then <...
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### Why is “1” not a valid variable? Why is there not a function plotted in the Plot function? [duplicate]

This is my code for playing this kind of stuff ...
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### Definite Integration with Exponental Heaviside Step Funtions

As part of an equation of state calculator that I am working on, I have to handle a virial expansion for the equation of state. As such I have to solve for the virial coefficent, $B(T)$, which is ...
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### After activating, inactive integral, output is coming same as input

I am trying to plot s w.r.t r (0,10). But because of inactive integral I am not able to. When I activate inactive integral, output is coming same as input. When I am trying to plot graph w.r.t r(0 to ...
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I'd like to implement a generic rule for expanding differential forms by the product rule. For instance, I'd like to transform the following PDE: $\phi \frac{\partial \phi}{\partial t} = \phi \nabla^... 1answer 31 views ### Compare their asymptotic behaviour using the order notation [closed] For each pair of the following functions, compare their asymptotic behaviour using the order notation. f(n) = e^n and g(n)= 3n^2 0answers 43 views ### Problem with antiderivative which involves DiracDelta Let us execute in version 12.0 Integrate[DiracDelta[x]*DiracDelta'[x], x] DiracDelta[x]^2/2 and this lasts at least since version 7. However, the ... 0answers 36 views ### Z-Transform Solution I am trying to solve the z-transform of the following sequence using Mathematica: x[n]=-a^n u[-n-1] The known result is$X(z)=z/(z-a)$with ROC:$|z|<|a|$. ... 0answers 46 views ### I need a starter kit for Differential Geometry In Modern Cosmology, the Geodesic Equation is described as:$$\frac {d^2x'^2}{dt}+\left[ \left( \{\frac{\partial x}{\partial x'}\}^{-1} \right)^l_i \frac{\partial^2 x^i}{\partial x'^j \partial x'^k} \... 0answers 96 views ### How do I solve the integral over four spherical harmonics? I want to solve this integral ... 2answers 316 views ### Siginificant speed difference of Integrate between 9.0 and 12.0 I just upgraded from 9.0 to 12.0, and I found some strange difference in timings for the following expressions: a. Integrate[Exp[-a*x^8],{x,-Infinity,Infinity}] b.... 0answers 45 views ### Derivative operator w.r.t a vector index and change of variables Description and code lines: Define a scalar product to represent A_i·A_j , A_i ·B_j and B_i ·B_j, such that A_i · A_i = 0. This is implemented in the following way: ... 1answer 40 views ### D: Understanding the output of 'n' th derivative of a function involving Exp I am trying to find the n^{th derivate of a function involving Exp as given below. ... 1answer 235 views ### Why the Kernel crashes on these integrals in V12? Reported to WRI, [CASE:4331819] This is using V12, on windows 10, 64 bit. Note: these integrals work OK on 11.3 on same PC. Any idea why the Kernel now crashes on these types of integrals? ... 1answer 76 views ### Reduce to Piecewise There are some similar posts on SE, but none of them seems to exactly address my issue. I need to integrate a rather complicated function (over x>1) separately over two domains defined as ... 1answer 65 views ### FindMinimum giving wrong answer [closed] I have a very simple problem that Mathematica is giving a wrong answer to. I want to minimize the following function: \frac{3+t^2+6\theta +3 \theta^2}{6 t^3} in \theta and t. Now, plotting the ... 1answer 61 views ### How to substitute by NDSolve solution to plot a new function Assume I got some function by NDSolve , like y(t) ... 3answers 323 views ### Solve command does not solve this equation! I tried to solve the following equation with Mathematica: \left(1-x^2\right) \left(n \left(x^4-2 x^2+5\right)-4 \pi \left(x^2-1\right)\right) \sinh (\pi x) \cosh (n x)+\sinh (n x) \left(\left(1-x^... 0answers 63 views ### How to solve this equation in Mathematica? I wonder what is the best way to solve this equation in MA?$$ y= \frac{\partial}{\partial x} ~ \frac{\partial}{\partial x^*} f $$where y and ... 1answer 75 views ### How to obtain the symbolic expression for the integral? I need to evaluate the following expression, \frac{1}{\Gamma(1-\alpha)} \frac{d}{d x} \int_{0}^{x}(x-t)^{-\alpha}(\exp(\lambda t)) d t, 0<\alpha<1, \lambda\in \mathbb{C} using Mathematica to ... 0answers 42 views ### Efficient application of the fundamental theorem of calculus How can the following definite integral be computed with Mathematica?$$ -\frac14\int_1^{\infty}\!\!\frac{\sqrt{-4 x^4-4 x^2 z-(y^2+z)^2}}{x (x^2+z)}\theta\!\left(-4 x^4-4 x^2 z-(y^2+z)^2\right)\... 0answers 130 views ### The most bizarre kernel crash ever. Kernel crash in Integrate under simple different setups. Unable to find cause Reported to WRI. CASE:4330461 V 12 on windows 10 64 bit. Note: This problem do not show up in V 11.3. Only in V12. For the last 2 hrs, I've been trying to zoom into why V12 kernel crash when ... 0answers 33 views ### Solving an integral using assumptions I am trying to solve the integral Integrate[(Sin(theta))/sqrt((r^2) + (s^2) - 2 rs(cos(theta))), {theta, 0, pi}] with assumptions that ... 1answer 58 views ### Computing the definite integral of a fractional polynomial containing sin(x) and x^n I need to compute the definite integral defined as $$\int_{-\infty }^{+\infty } \frac{\sin ({x_0}\, \omega )-\sin (x \omega )}{(\sin (x \omega )-\sin ({x_0}\, \omega ))^2+(x-{x_0})^2} \, dx\,.$$ When ... 0answers 95 views ### Complicated Integral output with Unfamiliar Regularized Hypergeometric Function I need the solution for following integral and it has output in MATHEMATICA as: ... 1answer 92 views ### Real and imaginary parts of complex logarithm I need to obtain the real and imaginary parts of the below expression with Mathematica:$(- i a - m^2) \ln(\frac{i m^2}{2 a})$, where$a$and$m\$ are real. So we have: ...
I'm trying to evaluate the triple integral $$\int_{0}^{1} \int_{0}^{1-x} \int_{0}^{1-\max(x,y)}1 dzdydx$$ in Mathematica. The code I'm using is simply ...