009B Sample Final 1, Problem 7

a) Find the length of the curve

$y=\ln(\cos x),~~~0\leq x\leq {\frac {\pi }{3}}$.

b) The curve

$y=1-x^{2},~~~0\leq x\leq 1$

is rotated about the $y$-axis. Find the area of the resulting surface.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Step 3:

(c)

Step 1:

Step 2:

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

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