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 $(4,73).$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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