EXAMPLE 5 Find the volume of the solid region bounded above by the paraboloid z = 9x² - y² and below by the unit circle

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Example 5 Find The Volume Of The Solid Region Bounded Above By The Paraboloid Z 9x Y And Below By The Unit Circle 1 (58.34 KiB) Viewed 15 times

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EXAMPLE 5 Find the volume of the solid region bounded above by the paraboloid z = 9x² - y² and below by the unit circle in the xy-plane. Solution The region of integration R is bounded by the unit circle x² + y² = 1, which is described in polar coordinates by r = 1,0 ≤ 0 ≤ 27. The solid region is shown in Figure 15.28. The volume is given by the double integral ff ( 9 - x² - y²) dA = ["²" [" 0 R 1 - LT = 2π = -1.³1% (9²) r dr do (9r r³) dr de 1 2π - 17/2 do - 177 = 2 de ² = x² + y², dA = r dr do.