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12

Artes' guess seems basically right. Here is a way to reach the correct result. First, the antiderivative returned by Mathematica: i0 = FullSimplify[ Integrate[Sqrt[(2 t)^2 + (4 - 3 t^2)^2], t], t > 0] (* (2 (Sqrt[16 - 2 I (-5 I + Sqrt[11]) t^2] Sqrt[8 + I (5 I + Sqrt[11]) t^2] ( 5 (-5 I + Sqrt[11]) EllipticE[ArcSin[1/2 t Root[9 - 5 ...


8

You can set the options for WolframAlpha in the usual way. The option to change is: SetOptions[WolframAlpha, PodStates -> {"Show metric"}] as for me (for whatever reason) it was the default to show metric units, I could verify with: SetOptions[WolframAlpha, PodStates -> {"Show non-metric"}] that this seems indeed to affect also the answers to the ...


8

Though WolframAlpha understands some basic Mathematica syntax, that is simply not it's first objective, namely to attempt to understand natural language input. Thus, rather than typing Integrate[x*Sin[x],{x,0,Pi}] one may type some variant of integrate xsinx x,0,pi The results, whether obtained via the web interface or right in notebook, are ...


6

In Mathematica 10, this tells you the number of calls remaining in your cloud account if you are logged in: CloudAccountData["WolframAlphaCallsAvailable"] 2168


5

Calling Wolfram|Alpha is not generally an efficient way to retrieve bulk data; where possible, it is better to use a built in data function. Part of the problem is figuring out what to submit to Wolfram|Alpha. In the code you supplied, the issue begins with Wolfram|Alpha returning Missing[NotAvailable]. WolframAlpha["AAPL ...


5

This does not really answer the question as to why Mathematica's Integrate yields an apparently wrong answer. But to simply state why the two answers are different. It seems Wolfram|Alpha does not attempt to do a symbolic integration (which is what your input asks for) before taking its numerical value. As I stated in my comment, using NIntegrate gives the ...


5

For indefinite integrals where "Show Steps" is available, the pod state is "IndefiniteIntegral__Step-by-step solution". The following works for cases where W|A can show the steps. showSteps[query_] := WolframAlpha[ "integrate " <> ToString[query], {{"IndefiniteIntegral", 2}, "Content"}, PodStates -> {"IndefiniteIntegral__Step-by-step ...


5

If you don't want Mathematica to use Wolfram | Alpha for correcting incorrect units, you can just set $AllowInternet = False. The downside of this is that it also blocks internet access for the curated data functions such as WeatherData, FinancialData, etc. You can also use Block to disallow internet only within your function.


4

A properly formatted Quantity expression should work just fine, without trying to connect to WolframAlpha servers for conversion. For example, Quantity[1, "Feet"] + Quantity[2, "Inches"] should run with or without internet connectivity. In contrast, Quantity[1, "Foot"] + Quantity[2, "Inches"] will attempt to contact WA servers in an attempt to ...


4

Here is how you attack this: First click on the little "+" in the right upper corner. Then you select either "Subpod content" or directly "Formula data". Both will result in a more specific request which gives you the hint you need: {WolframAlpha[ "6.38905609893065", {{"PossibleClosedForm", 1}, "FormulaData"}], WolframAlpha[ "6.38905609893065", ...


4

I can offer some ideas but it would take work to put together into a package. I'll illustrate with the example sqrt(3)+sqrt(5)pi. val = Sqrt[3] + Sqrt[5]*Pi; Set up an vector of values involving powers of both pi and val. We will work at fairly high precision (300 digits). I chose to go to degree 6 in each, which is overkill for this example but of course ...


3

Plot[2 x - Sinh[x], {x, -Pi, Pi}] FindRoot[2 x == Sinh[x], {x, #}] & /@ {-2, 0, 2} {{x -> -2.17732}, {x -> 0.}, {x -> 2.17732}}


3

This issue should now be resolved. If it isn't, please try restarting Mathematica, and try your input again. If this still fails, then please post the output of: PacletInformation["WolframAlphaClient"]


3

I observed this behavior while at a training session at Wolfram Headquarters, and there seems to be an issue with using Integers here: Integrate[Sqrt[(2. t)^2 + (4. - 3. t^2)^2], {t, 0, 2}] // N (* 7.847 *) Specifying Real numbers yields the correct result. I can only assume that Wolfram Alpha is performing this calculation with Real numbers as well.


3

You can use the RSolve command: RSolve[{a[n] == 1/2 (a[n + 1] + a[n - 1]), a[0] == 1, a[6] == 0}, a[n], n] {{a[n] -> (6 - n)/6}} {{a[n] -> (6 - n)/6}} /. n -> 3 {{a[3] -> 1/2}}


3

I have no idea why DateListPlot does not work with Quantity. Perhaps it's a bug? But the workaround is very easy: using pattern replacements we extract the numerical values. DateListPlot[nominal /. Quantity[x_, _] :> x, FrameLabel -> {"year", "$ per year"}] Browsing through the help, another option is QuantityMagnitude. ...


2

You can find the exchanges Mathematica knows about using: FinancialData["Exchanges"] From this you can extract the main London exchange name which is , "LSE". Then you can retrieve the available quoted entities: FinancialData["LSE", "Members"] Amongst those you will hopefully find most of the symbols which comprise the indices you might be interested ...


2

Before we look at how to generate the textual form, let's correct a syntax error in your code; function application in Mathematica is indicated by square brackets, so Sin(x + y) in your integral must replaced Sin[x + y]. With this change your integral evaluates correctly: We verify that the above is correct by taking the derivative with respect to ...


2

LinearModelFit[{{0,4},{4,20}},{1,x},x] worked for me


2

The currently accepted answer does not seem to be valid as of July 2014. I tested WolframAlpha calls with the following: properties = {"Abbreviation of ", "Alternate Names for ", "Atomic Number of ", "Atomic Radius of ", "Atomic Weight of ", "CAS Number of ", "Heat of fusion of ", "Stable Isotopes for ", "Universal abundance of ", "Discovery Year of ...


2

D[x^2 + x y[x] == 5, {x, 1}] sol1 = Solve[%, y'[x]] D[x^2 + x y[x] == 5, {x, 2}] sol2 = Solve[%, y''[x]] sol2 /. sol1 // Simplify


1

As suggested by kguler, using Piecewise is easiest; however, you can also use Show or Boole. Show[ Plot[(2*x), {x, 1, 3}], Plot[(x^2), {x, 3, 5}], PlotRange -> All, AxesOrigin -> {0, 0}] Plot[ 2 x Boole[1 < x < 3] + x^2 Boole[3 < x < 5], {x, 0, 5}, AxesOrigin -> {0, 0}, PlotStyle -> Red]


1

The functionality to download the components of the FTSE 100 used to be available in Yahoo Finance, but it is not available anymore. E.g. Download a CSV of the constituents of the FTSE-100 from Yahoo Finance FinancialData uses Yahoo, so that explains why it doesn't work. Finding another source from which to download a list has proved tricky. There is a ...


1

What you want to do is to interpolate between values, WA understood this easily:


1

To get just the nutrition facts for simpler data use: WolframAlpha["1 whole wheat tortilla + 2 slices american cheese + 150 g steak", {{"NutritionLabelMultiplePlus", 1}, "Content"}] To understand how to get this code use this answer as guide. That other 2nd entry is so complex and long it throws something off in formatting. You can send feedback to ...


1

This is not an answer, but comparing the answer with Maple, and also showing step by step integration using Rubi, which might help point to where Mathematica went wrong. Mathematica Integrate r = Simplify@Integrate[Sqrt[(2 t)^2 + (4 - 3 t^2)^2], t] N[r /. t -> 2 - r /. t -> 0, 20] Maple r:=int(sqrt( (2*t)^2+(4-3*t^2)^2),t=0..2); ...



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