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Is W.Alpha calculating double integrals incorrectly? Why is this happening?

Posted 10 years ago

I tried typing this into the wolfram alpha app " ??xcosy dydx , y from 0 to x^2 , x from 0 to 1 " I got an answer of " sin^2(1/2)= 0.2298.. " But the answer (as far as I can tell) should be 0.5 What's happening here?

POSTED BY: A Afif
6 Replies
Posted 10 years ago

Guys , thank you. It's my bad , I just made a miscalculation that's all , I will be more careful before posting next time.

POSTED BY: A Afif

I caluculated "by hand" and get 0.229849 too.

POSTED BY: Juerg Baertsch

Did you integrate by parts?

POSTED BY: Frank Kampas

enter image description here

POSTED BY: Juerg Baertsch
Posted 10 years ago

Thanks for your reply Baldwin , it was just a miscalculation. I'm sorry

POSTED BY: A Afif
Posted 10 years ago

Why do you believe that the result should be 0.5? A brute-force check by dividing up the unit square into 10,000^2 little squares and summing up the contributions from the appropriate squares gets me a value of 0.22992. In Mathematica 10 I get the following:

In[4]:= Integrate[x Cos[y], {x, 0, 1}, {y, 0, x^2}]
NIntegrate[x Cos[y], {x, 0, 1}, {y, 0, x^2}]

Out[4]= Sin[1/2]^2

Out[5]= 0.229849
POSTED BY: Jim Baldwin
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