009B Sample Final 2, Problem 5

(a) Find the area of the surface obtained by rotating the arc of the curve

$y^{3}=x$

between  $(0,0)$  and  $(1,1)$  about the  $y$-axis.

(b) Find the length of the arc

$y=1+9x^{\frac {3}{2}}$

between the points  $(1,10)$  and  $(4,73).$

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Solution

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