GATE 2020 BM – Question 56
Evaluate $\iint_Rxy\,dx\,dy$ over the first-quadrant part of the unit disc, to three decimals.
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Show answer and explanation
Correct answer: 0.125 to 0.125
Explanation
Use polar coordinates x=r cosθ,y=r sinθ and area element r dr dθ. The integral separates into ∫₀¹r³dr×∫₀^{π/2}sinθcosθdθ=(1/4)(1/2)=1/8=.125. The extra radial factor from the Jacobian is required.