Disc Example Problem

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Situation: You need to find the volume of the solid formed by revolving the region bounded by the graph of f(x) = SQRT(sin x) and the x-axis (0 < x < pi) about the x-axis.


Solution:From the representative rectangle above, you can see that the radius of this solid is R(x) = f(x) = SQRT(sin x). In turn, the volume of the solid of revolution is
             _{b                           pi}
V = pi §  [R(x)]² dx = pi §  (SQRT(sin x))² dx
             ^{a                           0}
          _pi
= pi §  sin x dx
          ⁰
                   _pi
= -pi cos x]
                   ⁰
= pi(1 + 1)

= 2pi.