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Multiple Integrals

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Chapter 1 Multiple Integrals I.1 Double Integrals 1. Use the Midpoint Rule to estimate the volume under f (x, y) = 4x + 8y and above the rectangle given by 0 ≤ x ≤ 4, 2 ≤ y ≤ 6 in the xy-plane. Use 4 subdivisions in the x direction and 4 subdivisions in the y direction. 2. Use the Midpoint Rule to estimate the volume under f (x, y) = 4x − y 2 and above the rectangle given by 0 ≤ x ≤ 2, −2 ≤ y ≤ 1 in the xy-plane. Use 2 subdivisions in the x direction and 3 subdivisions in the y direction. 3. Compute these iterated integrals: Z 1Z 4 x dy dx (a) 0 0 Z 1Z 4 x dx dy (b) 0 0 ...
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