Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 3 / 3A / Solution Created 2026-09-23 Updated 2026-09-25
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Set
(1)
Because the region lies in the positive quadrant, its four inequalities become
(2)
Thus this change of variables sends to a rectangle in the -plane. Its Jacobian determinant is
(3)
so
(4)
Since , the double integral is
(5)
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