Let%20D%20be%20the%20(rotated)%20square%20in%20R%5E2%20with%20vertices%20(%2B%2F

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Let%20D%20be%20the%20(rotated)%20square%20in%20R%5E2%20with%20vertices%20(%2B%2F-1%3B0)%20and%20(0%3B%20%2B%2F-1).%20Let%20f(x%3B%20y)%20%3D%205%2C%20g(x%3B%20y)%20%3D%20xy%2C%0Aand%20h(x%3B%20y)%20%3D%20y%5E2.%20Compute%20the%20double%20integrals...%0A%0A%0AHint%3A%20Pay%20attention%20to%20the%20geometric%20meaning%20of%20the%20double%20integral%20in%20terms%20of%20signed%20()%20volumes%0Abeneath%20graphs%20over%20regions.%20Using%20this%20interpretation%2C%20the%20value%20of%20the%20rst%20two%20double%20integrals%0Acan%20be%20determined%20without%20integrating%20(!)%2C%20while%20the%20last%20can%20be%20determined%20with%20only%20a%20single%0Aiterated%20integral%2C%20despite%20the%20complexity%20of%20the%20region.

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