NYJC/2013/I/Q11 Finding Area and Volume of Parametric Equations

The curve C is defined by the equations 

(i) Sketch C, showing all axial-intercepts and endpoints clearly.

(ii) Using the fact that C is periodic with period 2π, or otherwise, find the exact area enclosed by C, the line x=-2π, x=2π and the x-axis. 

(iii) C1 is the part of the curve C for π≤θ≤2π. The region R is bounded by C1, the axes and the line y=2. State the area of R. 

(iv) Find the volume of the solid formed when R is rotated through 2π radians about the y-axis, giving your answer to 1 decimal place. 

(v) Find the volume of the solid formed when R is rotated through 2π radians about the x-axis, giving your answer to 2 decimal places. 

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