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 5 months ago
Hi,
I'm looking at Part I of Problem Set 7 on Double Integrals. It's the supplementary problem 3A6.
I tried approaching the question by visualising the integrand in 3D and how it cuts region R in the xy plane. It worked for the first three integrals but the last three threw me off. I checked the answers but I still cannot understand them.
Is there a better way to approach these questions? And if possible, explain how the last three integrals can be solved.
Thank you!
 5 months ago
Hi, I'm looking at Part I of Problem Set 7 on Double Integrals. It's the supplementary problem 3A6. I tried approaching the question by visualising the integrand in 3D and how it cuts region R in the xy plane. It worked for the first three integrals but the last three threw me off. I checked the answers but I still cannot understand them. Is there a better way to approach these questions? And if possible, explain how the last three integrals can be solved. Thank you!

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Nicholaslow
 5 months ago
Best ResponseYou've already chosen the best response.0The question link : http://ocw.mit.edu/courses/mathematics/1802scmultivariablecalculusfall2010/3.doubleintegralsandlineintegralsintheplane/partadoubleintegrals/problemset7/MIT18_02SC_SupProb3.pdf The answer link: http://ocw.mit.edu/courses/mathematics/1802scmultivariablecalculusfall2010/3.doubleintegralsandlineintegralsintheplane/partadoubleintegrals/problemset7/MIT18_02SC_SupProbSol3.pdf

Nicholaslow
 5 months ago
Best ResponseYou've already chosen the best response.0omg ok. I managed to solve them using the mathlet that plots 3D graphs. The volumes cancel out nicely for: \[\int\limits_{}^{}\int\limits_{}^{} x ^{2}y\ dA\] \[\int\limits_{}^{}\int\limits_{}^{} xy\ dA\] Then for \[\int\limits_{}^{}\int\limits_{}^{} x ^{2 } +y\ dA\] I realized I could take out y from the integrals which reduces to \[\int\limits_{}^{}\int\limits_{}^{} x ^{2}\ dA\] + \[\int\limits_{}^{}\int\limits_{}^{}y\ dA\] the second integral being zero. If anyone has a smarter way to solve without using the mathlet please let me know.
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