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Unformatted text preview: Math 2433 – Notes week 11 (16.4-16.6) Popper011 1. What problem did Leonardo da Vinci, Winston Churchill, Albert Einstein, Thomas Edison and General George Patton have in common? A. All were dyslexic. B. All had false teeth C. They were all blind 2. Which of the following people were not members of the Rolling Stones? A. Mick Jagger B. Bono C. Keith Richards D. Bill Wyman 3. Evaluate the integral taking Ω : 0 < x < /2, 0 < y < /2. a) b) c) d) e) 16.4 The Double Integral as a Limit of Riemann Sums; Polar Coordinates Given ( ) , F F r θ = continuous on : , a r b α θ β Γ ≤ ≤ ≤ ≤ Partitions: 1 2 1 2 ... ... n n a r r r r b α θ θ θ θ β < < < < < < < < < < < < Recall, polar area is found by: So, the area of our “bases” will be “polar rectangles” with This means our Riemann Sums will be: * * 1 1 1 ( , ) 2 m n i i i j i j j i r r F r r θ θ- = = + Δ Δ ∑∑ And ( , ) ( , ) b a F r r drd F r r drd β α θ θ θ θ Γ = ∫∫ ∫∫ The double integral of ( )...
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- Fall '10
- Riemann Sums, double integration, A. Mick Jagger B. Bono C. Keith Richards D. Bill Wyman