Washer Example Problem

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Situation: You must find the volume of the solid formed by revolving the region bounded by the graphs of y = SQRT(x) and y = x² about the x-axis, as shown below.


Solution: As seen in the images above, you should notice that the outer and inner radii are as follows.

Outer Radius
R(x) = SQRT(x)

Inner Radius
r(x) = x²

Integrating between 0 and 1 produces
             _b
V = pi §  ([R(x)]² - [r(x)]²) dx
             ^a

          ₁
= pi §  (x - x⁴) dx
          ⁰
                           ₁
= pi [x²/2 - x⁵/5]
                           ⁰

= (3pi)/10.