GATE EE 2022 Set 1 — Question 52
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Engineering Mathematics → Vector Calculus → Gradient, Divergence & Curl
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Question
Let . The value of , where is the volume enclosed by the unit cube defined by , is
Correct answer
(C) 10
Solution
Given the vector field .According to the divergence theorem, the volume integral of the divergence of a vector field over a volume is:First, calculate the divergence of :Now, evaluate the volume integral over the unit cube defined by the limits :Since the integrand depends only on , the triple integral can be simplified as:Thus, the value of the integral is 10. The correct option is (C).
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