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Nicholaslow

  • 5 months ago

Hi, I'm looking at Part I of Problem Set 7 on Double Integrals. It's the supplementary problem 3A-6. I tried approaching the question by visualising the integrand in 3D and how it cuts region R in the x-y 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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  1. Nicholaslow
    • 5 months ago
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    omg 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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