Double integration over a region

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SUMMARY

The discussion centers on evaluating the double integral ∫∫ (2x+4y+1) dA over the region defined by the curves y = x² and y = x³. The correct setup for the integral is confirmed as ∫^{1}_{0} ∫^{x^{2}}_{x^{3}} (2x+4y+1) dydx. The participant expresses initial uncertainty but ultimately receives reassurance from another user, Zondrina, confirming that their setup is accurate.

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Homework Statement



∫∫ (2x+4y+1) dA, R: y = x[itex]^{2}[/itex], y = x[itex]^{3}[/itex]

Homework Equations



R∫ f(x,y) dA

The Attempt at a Solution


Since there was no direct question, I assumed to just evaluate with whatever I was given.

I would really like to make sure that my integrals are set up correctly:

[itex]∫^{1}_{0}[/itex] [itex]∫^{x^{2}}_{x^{3}}[/itex] (2x+4y+1) dydx
 
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aaronfue said:

Homework Statement



∫∫ (2x+4y+1) dA, R: y = x[itex]^{2}[/itex], y = x[itex]^{3}[/itex]

Homework Equations



R∫ f(x,y) dA

The Attempt at a Solution


Since there was no direct question, I assumed to just evaluate with whatever I was given.

I would really like to make sure that my integrals are set up correctly:

[itex]∫^{1}_{0}[/itex] [itex]∫^{x^{2}}_{x^{3}}[/itex] (2x+4y+1) dydx

EDIT : Wow read that wrong I am half asleep. Sorry. Looks good.
 
Last edited:
LOL...great! I was reading all through my text and ready to call it quits! Thank you Zondrina.
 

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