GATE ME 2020 Set 2 — Question 13
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Engineering Mathematics → Multivariable Calculus → Change of Order of Integration
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Question
Let . Then, may also be expressed as
Correct answer
(C) ∫_(y=0)¹ ∫_(x=√(y))¹ xy² dx dy
Solution
The given integral is . The region of integration is bounded by . To change the order of integration, we first determine the limits for . The maximum value of is , so .
For a fixed , varies from the curve (which is ) to the line . Thus, the integral becomes . This corresponds to option (C).
For a fixed , varies from the curve (which is ) to the line . Thus, the integral becomes . This corresponds to option (C).
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