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?
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
Thanks for your reply Baldwin , it was just a miscalculation. I’m sorry
I caluculated “by hand” and get 0.229849 too.
Did you integrate by parts?
Guys , thank you. It’s my bad , I just made a miscalculation that’s all , I will be more careful before posting next time.