Exam 12: Extension B: Multiple Integrals

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Evaluate the integral by reversing the order of integration. Evaluate the integral by reversing the order of integration.

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Evaluate the double integral. Evaluate the double integral.     is bounded by   and   Evaluate the double integral.     is bounded by   and   is bounded by Evaluate the double integral.     is bounded by   and   and Evaluate the double integral.     is bounded by   and

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Evaluate the integral by reversing the order of integration. Evaluate the integral by reversing the order of integration.

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Find the volume under Find the volume under   and above the region bounded by   and  and above the region bounded by Find the volume under   and above the region bounded by   and  and Find the volume under   and above the region bounded by   and

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Evaluate the double integral. Evaluate the double integral.   ,   is triangular region with vertices   , Evaluate the double integral.   ,   is triangular region with vertices   is triangular region with vertices Evaluate the double integral.   ,   is triangular region with vertices

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Evaluate the double integral Evaluate the double integral   ,where   is the region bounded by the graphs of   and   ,where Evaluate the double integral   ,where   is the region bounded by the graphs of   and   is the region bounded by the graphs of Evaluate the double integral   ,where   is the region bounded by the graphs of   and   and Evaluate the double integral   ,where   is the region bounded by the graphs of   and

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Evaluate Evaluate   where   is the figure bounded by   and   where Evaluate   where   is the figure bounded by   and   is the figure bounded by Evaluate   where   is the figure bounded by   and   and Evaluate   where   is the figure bounded by   and

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Calculate the iterated integral. Calculate the iterated integral.

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Evaluate the double integral. Evaluate the double integral.     is bounded by the circle with center the origin and radius   Evaluate the double integral.     is bounded by the circle with center the origin and radius   is bounded by the circle with center the origin and radius Evaluate the double integral.     is bounded by the circle with center the origin and radius

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Evaluate the iterated integral Evaluate the iterated integral   by reversing the order of integration. by reversing the order of integration.

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