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Sum is not working in Wolfram|Alpha: use different phrasing or notations

Posted 22 days ago
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Hi, I used Wolfram|Alpha Pro Premium for Educators.

Please why this work:

plot Integrate[\(40)Sum[Sin[mπx]Sin[πy],{m,1,3}]\(41)*\(40)Sum[sin\(40)kpix\(41)sin\(40)kpiy\(41),{k,1,3}]\(41),{y,0,1}],x=0:1

but this not? (give me the message: Try the following: Use different phrasing or notations...)

plot Integrate[\(40)Sum[Sin[mπx]Sin[mπy],{m,1,3}]\(41)*\(40)Sum[sin\(40)kpix\(41)sin\(40)kpiy\(41),{k,1,3}]\(41),{y,0,1}],x=0:1


POSTED BY: mazen khoder
Posted 21 days ago


Plot[Integrate[Sum[Sin[m π x]*Sin[m π y],{m,1,3}]*Sum[Sin[k π x]*Sin[k π y],{k,1,3}],{y,0,1}],{x,0,1}]

seems a little too complicated for Wolfram|Alpha to understand and do in one step.

So do this simpler problem first.

Sum[Sin[m π x]*Sin[m π y],{m,1,3}]*Sum[Sin[k π x]*Sin[k π y],{k,1,3}]

which returns

(Sin[π x] Sin[π y] + Sin[2 π x] Sin[2 π y] + Sin[3 π x] Sin[3 π y])^2

You can then slide your mouse over the line just below Input Interpretation and at the right end of that click on the orange Plain Text and copy that result into your clipboard.

Note one little related item, if I haven't made a mistake then I think the product of those two sums is equal to the square of either one of those sums and shorter inputs are sometimes easier for Wolfram|Alpha to understand and correctly calculate, but for this problem that doesn't help enough for Wolfram|Alpha to solve your problem in a single step.

Sum[Sin[m π x]*Sin[m π y],{m,1,3}]^2

Then you can paste your clipboard contents back into the Wolfram|Alpha input box like this

Integrate[(Sin[π x] Sin[π y]+Sin[2 π x]Sin[2 π y]+Sin[3 π x] Sin[3 π y])^2,{y,0,1}]

That is complicated enough that the free version of Wolfram|Alpha can't do it in the time available, but the pro version might give you a little more time and tell you that the result is

(3+3 Cos[2 π x]+Cos[4 π x]) Sin[π x]^2

Again you can do the copy and paste that result back into WolframAlpha like this

Plot[(3+3 Cos[2 π x]+Cos[4 π x]) Sin[π x]^2,{x,0,1}]

and get the graph you are looking for.

This trick of dividing a complicated problem into multiple simpler steps and using the result from each of those steps to get the result you want from WolframAlpha is powerful and useful.

I hope it works for you.

POSTED BY: Bill Nelson
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