## devops – Is Continuous Integration nowadays intended as “Continuous Inspection”?

I’ve been reading a log about CI (mostly Addison-Wesley books) and taking “CI” courses. I see two clear distinctions between old books on CI and new ones:

• Old ones focus on “committing” or “pushing” your code often (integrating often)
• New ones talk about practices for having feedback early in the process, like running builds and tests in a pull request instance.

I think it’s not common nowadays to commit or push every day (or multiple times per day), but it’s a great practice to build and run tests in every pull request. Is it still Continuous Integration? Or am I missing something?

## integration – Stuck at an integral

So I’m trying to find a volume of a surface and a cylinder. I managed to do it with cylindrical coordinates. But I wanted to try to without it, but the integral is seriously hard. So the integral was

$$V=int^2_{-2}int^sqrt{4-x^2}_{-sqrt{4-x^2}}int^{4-x^2}_0dzdydz$$

Using the symmetri and the fact that our function is even

$$V=4int^2_0int^sqrt{4-x^2}int^{4-x^2}_0dzdydx$$

I manged the last part

$$V=4int^2_0(4-x^2)left(sqrt{4-x^2}right)dx$$

I first used integration by parts where $$u = (4-x^2)^{frac{3}{2}}$$and $$dv=1$$ and ended up with
$$I = 4left(xleft(4-x^2right)^{frac{3}{2}}-int-3x^2sqrt{4-x^2}dxright)$$

This is where I’m stuck, clearly u-substitution wouldn’t work. Some help would be greatly appreciated!

## differential equations – How to integrate ParametricNDSolve solution and solve for parameter based on integration result

I have a second-order ODE that depends on a parameter $$rho_0$$. For a given $$rho_0$$, I can use NDSolve or ParametricNDSolve to get the solution $$y(r; rho_0)$$ very easily, but I want to solve for the value of $$rho_0$$ that satisfies the following (admittedly complicated) condition:
$$4pirho_0int_0^Rr^2 e^{-y(r; rho_0)} dr = M$$
where M and R are given.

I’ve tried doing this several different ways, using different combinations of (Parametric)NDSolve(Value), NSolve, and FindRoot, and trying solutions from several related posts on here, but I just can’t get it to work. Here’s one such trial:

sol = ParametricNDSolveValue(
{y''(x) + 2/x * y'(x) == (chi(rho0) * y'(x)^2 + 1)/(chi(rho0) + Exp(y(x))),
y(ibc) == 0, y'(ibc) == 0}, y, {x, ibc, obc}, {rho0})

FindRoot((4 Pi * rho0 *
NIntegrate( r^2 * Exp( -sol(rho)(r/r0(rho)) /. rho -> rho0 ), {r, 0, R} )
- M), {rho0, rho0guess})


where rho0guess, chi, and r0 are all defined in advance. When I run this, I get the following error message

NIntegrate::inumr: The integrand E^-ParametricFunction(1,InternalBag(<1>),0,1,{<<1>>},{NDSolvebase$189416,NDSolveNDSolveParametricFunction(0,<<8>>,All)})(rho0)(<<1>>/Sqrt(<<1>>)) r^2 has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,95.908}}.  I think the problem is that NIntegrate is trying to evaluate the solution before a value for rho0 is passed to the solution by FindRoot, and so it’s failing to integrate because rho0 doesn’t have a numerical value yet. I just can’t figure out how to get around this. Any help is much appreciated! EDIT: Here are some typical values of the various parameters and functions GAU = 4.3*10^-6; rhobAU = 135.3; M = 10^11; R = (M/(4 Pi/3*200*rhobAU))^(1/3); R0 = 4; kTm = GAU*M/R/2; r0(rho0_) := Sqrt(kTm/(4 Pi*GAU*rho0)) chi(rho0_) := R0^2/(Pi^2*r0(rho0)^2) rho0guess = 10^8;  ## Integration of compactly supported forms Now that school is over I do not feel bad asking questions here. I did not really understand the relationship between integration of forms and differentiation. I was asked to prove that a compactly supported k-form w on $$R^k$$ is the exterior derivative of a compactly supported k-1 form if and only if $$int_{R^k} w = 0$$. I thought the reverse direction could be solved by stokes theorem but now i am not sure. Not to mention that I dont know how to do the forward direction. I have considered projection w onto the k-sphere to get some w’ and we know w’=dv for some v on the sphere by a lemma from lecture. I dont know if this helps. ## numerical integration – NIntegrate::slwcon and NIntegrate::eincr: I have the following code to evaluate the double integral of which the integrand contains summations. a = 1.1798710705178221747709894550582188967078238417029640017201995589 3552025364542807472418914015859414022112280461408148970194496741533076 882157607415223127492391019655558195361182929703459158. 94383771058207*^12; b = 2.26562500; c = 1.81505148861869*^-11; d = 23.662621294619998242971428558039280847039065920403134745951781161 6604691248947208857758189787681405721656941282488226858308051995862227 03295794982365258929783937779449526906107493517940605539567157. 52081186501843; f = 3.9762816693358413444242383928332521659243792714105963808597582172 1677895928488587525623222082345413892578490996192857648555810218065386 055620034160228548784193009119494778657256763157.54308182919476*^-13; g = 3.1306512217343699049816678338611844042940126102861569115946355055 2379739233549991684436932580097276616360046758705039003579253070583704 87306284924487233677956546263347280851687424154.55339124819713*^-283; h = 0.4663677854613281996964274099654771725449995576718401982649626901 4979290048497524493727931929716644258598652635846126429619061653535457 7552234258390027879122494699655811617457309249292766647653158. 10068151409945; k = 1.7400621010179746539715325376531540776673407694803313887835074772 7621820290231417060167325520004426731623808979659285973341841054088991 377348701663084581319054270584192856482987849158.6501729599253*^-13; L = 12; p = 1.7267086550014064377504396122758581898174212801982663320383980364 4189130935666171318482175845230982997098739340274603421154239660049599 7742129919272319043201530223139294218906027174185411646792156. 9155606199771*^-19; m = {193.1974795021252244647940778330697265346831202988930438449952777 2307847128160223047093925434704114309184915713826376925945458184231453 466263054478004310746486964933973801043322148.30510799763482, -1.9831415769102246753169203737597186440257929720747405282387824878992 6107613692269553118408251584641941543185280916783314001387339467872143 8413408725537146318896037644145148.23545499521762*^14, 9.27130443465927962680463415680935518438025048895563739033406430779 2196012034144989441708086252518980765588393670969227402958335184629953 81754195556168420354856191202632726995515843148.1802144267804*^25, -2.5800039865768300579393918422060974207019853041395228305982709910784 5385543803983822395718755270344540849858353480555085709766499883993525 5692481465734198491137803554398276148.1336524600536*^37, 4.74051682958982877757253604628388253288384781482056602069781764081 9228970772949442973000148032178390675200697268768942345714056423740914 80354727904019873987134563343319805735897818842148.09340643440623*^ 48, -6.045696336170963761979351988393444721239513638248359564313546590 9718715772107181860271630911859080048890550740293482441710924532226834 88785001561949827887583104602354991010789148.05796717887392*^59, 5.48169129849067708749576724703553417939408966217748199411635112509 3975998785626154086737477706943924734870295242554891109862338634996706 52881122759735494841981860519139551755923247573972148.02635144833272*^ 70, -3.558859598535019932696238577795555409895936844852263611105033721 0375255058472565008180720204152692875351619018996231358541261075464815 50993035152346687208320263348602766130493464147.99786882797923*^81, 1.64170225303118668483536395284823903373718786459586837660122032491 6095608079033229473848757844731529141963765405064759781082803855127965 2691286574811194198800983167974295147.97199851695797*^92, -5.2480764106579160571712590401723827187713866001169686217276690968556 0720450830001550831782374704062930304936342651979107670945180568135634 934777787696977134688463363076848049109484147.94833381460728*^102, 1.10376762837378400256596151856877143314949611822933817186964398056 6513468174587221258709945187779831909161277645871738123234551311287274 78355158886780258679136222861840141147.92655298710872*^113, -1.3717147483659623561567398067035113741497860704561052158773749470395 4451131015780543446068263484385374754209550914285685014429230059159675 6883122631756455319026263237240593696821711147.9063994508292*^123, 7.62038321127089845343261988865253586612439689357390721954186078231 7745858168312353448416091122119241968300105088661006951809593285174538 28785418554487594420138798900387611147.8876665311791*^132}; n = {1.355573243087520514288089562497260829417934974879258545226394709 1581632390251949362448991535838854387828992200011014212046924115116342 36774361520751754411719411168290762941843303838260921034729154. 7068137372351, -1.0245928740767489003861056984284775651988428602209840685472503196463 8795930234592796835719935424571882137914261342592202874852760076112574 416630451012360208651254471215128194043516110717153.94630606168067*^ 13, 8.9274486445716723149532799214464202934486639009370371697876732811 7309338540881124740225222195651232772519644118676062290969039522944619 182163951555475885638710858185564149165684843153.80921876999915*^25, -3.6759676683395569226361903550968200824615587798139936187422973093672 7524993405149619110906669196324634865139505465691286936359213505175950 82648234290038347371835858805085681153.70951619258835*^38, 8.46890235524130159449486145084290474315429938343042316420562067986 2851660903090850781750760926753333681142269036924244448156733221457952 7284650316472932006583589556818127479776452351575153.63641768743574*^ 50, -1.183963727932234048419892914574504119691001960215443363374579536 6221799023716788793836145690916125278181883509910251692260914506526151 991183549806618069041478638356123410370047646153.58049547400296*^63, 1.05061217672427573937875620745709379002627336725498531970829595877 3024659127091166260173635393986216201350663927669330845944472454001554 7653381517564746234073087737793092403156290468681009911153. 53584270924242*^75, -6.0584630947562597856380562413442419518448978885525607665447920472335 7004600791968921362280443938576083533065571634125571548632808959929629 790577441227915620375110110148244720464105958153.4990714580894*^86, 2.28274980013156097133562209543324362618017404654189411106310354580 1316698809067147502956432483851929920100534744472639286623024080167418 0951137035977035828949374744764910684041153.46810663882243*^98, -5.5393276975669543411312359391170032422891499208542799478529688449103 0657737312682644055014461777520413955788265776706075897708285932473509 487959913970225597988826267142550230756354142547153.44158425404342*^ 109, 8.289929266459807127028509719838011396311076683133447742366507269 1426222477306422877783169874953638427457706706377785690078513120930488 09383654486564976662124022080955027406652237153.41855789644956*^120, -6.9209387452305809520831335905017476070978872825599662420473808654194 8931991860905633911584754872433560379615186289074673651242807441129188 233340512050802389488222073074566318608837938629357153. 39834390904957*^131, 2.45300100486846411742403054500030433066570931665654433746550128485 1080592792054839789289213596711427047642684395418250860055631043057336 48562402527422622838036053732378834470177372153.3804328940518*^142}; NIntegrate(!( *UnderoverscriptBox(((Sum)), (i = 0), (98))( *FractionBox(( *SuperscriptBox(((a*x + b)), (i))* Exp((-((a*x + b))))), (i!)) ( *UnderoverscriptBox(((Sum)), (i = 0), (L)) *FractionBox(( *SuperscriptBox(((y + x - c)), (d)) Exp((-((y + x - c)))/ f) ((m(((i + 1))) *SuperscriptBox(((y + x - c)), (i))))), (g)) ( *UnderoverscriptBox(((Sum)), (i = 0), (L)) *FractionBox(( *SuperscriptBox((y), (h)) Exp((-y)/k) ((n(((i + 1))) *SuperscriptBox((y), (i))))), (p)))))), {x, c, Infinity}, {y, 0, Infinity}, Method -> {"GlobalAdaptive", "MaxErrorIncreases" -> 4000}, MinRecursion -> 10, MaxRecursion -> 30)  However, I get two error messages, which are 1. NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. 2. NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 4000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained 0.9999763600200141and 0.0000461755863201869 for the integral and error estimates. I have tried to increase MaxErrorIncreases to 20000. However, the above two error messages still exist. Why these errors happen? Is there a method to fix these issues? ## Magento 2 admin panel integration is missing does anyone know how to fix a system error. I have asked someone to install Magento 2, but it seems like the system integration section is missing. Anyone know how to fix this problem? Thank you! ## plugins – wecashup payment integration with wordpress I use wecashup plugin to use in my wordpress website as payment gateway I create user in wecashup site and get merchant id ,secret and public id but when i enter place order it can’t get any response How integrate wecashup plugin for developers in wordpress ?? ## integration – Computing$displaystyle int_{0}^{1} x^2 sin(2pi nx)sin(2pi mx) dx\$.

I would like to know if there is any easy way or known formula to compute the following integral. For $$n,m in mathbb{N}$$, for $$n neq m$$, $$displaystyle int_{0}^{1} x^2 sin(2pi nx)sin(2pi mx) dx$$. I tried various graphs for $$nne m$$, and it seems the answer is $$0$$. That’s why I thought there might easy way to deal with this. Thanks.

## Problem with Integration – Mathematica Stack Exchange

I want to integrate a function which seems to have no regularity problems. In fact I have defined

K(x_, y_) :=
Assuming(Element({x, y}, Reals) && x > 0 && y > 0,
NIntegrate(Sqrt(1 - (Cos(x)*Cos(y) + Sin(x)*Sin(y)*Cos(t))^2), {t, 0, 2*Pi}))
R(x_, 0) := (x - Pi/2)^2
H(x_, 0) :=
Assuming(Element({x}, Reals) && x > 0, NIntegrate(Sin(t)*K(x, t)*R(t, 0), {t, 0, Pi}))


If I plot, the function I obtain a good output

Sin(x)*Exp(-10*H(x, 0)


But if I try to integrate it, even with NIntegrate I receive the following error messages

NIntegrate::inumr: The integrand Sqrt(1-(Cos(t) Cos(x)+Cos(t) Sin(t) Sin(x))^2) has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,6.28319}}.
General::stop: Further output of NIntegrate::inumr will be suppressed during this calculation.
NIntegrate::write: Tag Times in -Abs(t) is Protected.
General::stop: Further output of NIntegrate::write will be suppressed during this calculation.
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in x near {x} = {0.0217285}. NIntegrate obtained 2.897189900542515*^-18 and 3.722470516152078*^-24 for the integral and error estimates.
`

why is that?

## calculus – Need help in understanding the integration part of this question

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