SOLUTION: Set up but do not evaluate the integral of the function f(x,y)=cos(x^2+y^2) over the region R bounded by the curves x=y^3 and y=x

Algebra ->  Rational-functions -> SOLUTION: Set up but do not evaluate the integral of the function f(x,y)=cos(x^2+y^2) over the region R bounded by the curves x=y^3 and y=x      Log On


   

Question 1111423: Set up but do not evaluate the integral of the function f(x,y)=cos(x^2+y^2) over the region R bounded by the curves x=y^3 and y=x
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I think this is what you're asking.
Graphing the functions provided, find the limits of integration,
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Then,
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Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!
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Half of this integral is the double integral of the function cos%28t%5E2%2By%5E2%29%2Adt%2Ady over the following domain:


    The exterior integral is over  "y"  from   0  to   1.


    The interior integral is over  "t"  from  y^3  to  y.


The solution by the other tutor is   I N C O R R E C T.

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For the person who studies Calculus,  it is  VERY important  to learn on how to solve / (to setup)  such problems correctly.