1. (a) Sketch the graphs of 2 2sin ( ) yx = and 2 2cos ( ) yx = fromxπ =− to xπ = . [2 marks] (b) Using a double integral, calculate the area enclosed by the curves in the interval 0 x= to 4xπ = . [4 marks] (c) Using either a double integral, or a symmetry argument,

| April 14, 2018

1. (a) Sketch the graphs of 2 2sin ( ) yx = and 2 2cos ( ) yx = fromxπ =− to xπ = . [2 marks]  (b) Using a double integral, calculate the area enclosed by the curves in the interval 0 x= to 4xπ = . [4 marks]  (c) Using either a double integral, or a symmetry argument, determine the area enclosed by the curves in the interval 4xπ = to 2xπ = . [3 marks]  (d) Infinitesimal elements of volume are expressed in Cartesian coordinates by dV dxdydz = .  Using a tr … 

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