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Today's calculation of Integral 705

Source: 2011 Nagoya City University entrance exam/Architecture etc.

June 8, 2011
calculusintegrationtrigonometrycalculus computations

Problem Statement

The parametric equations of a curve are given by x=2(1+cos⁡t)cos⁡t, y=2(1+cos⁡t)sin⁡t (0≤t≤2π)x = 2(1+\cos t)\cos t,\ y =2(1+\cos t)\sin t\ (0\leq t\leq 2\pi).
(1) Find the maximum and minimum values of xx.
(2) Find the volume of the solid enclosed by the figure of revolution about the xx-axis.
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