Difference between revisions of "009B Sample Final 1, Problem 7"

Revision as of 22:07, 1 February 2016

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)

(b)

Step 2:

Step 3:

(c)

Step 1:

@@ Line 1: / Line 1: @@
-::<span class="exam">a) Find the length of the curve
+<span class="exam">a) Find the length of the curve
 ::::::<math>y=\ln (\cos x),~~~0\leq x \leq \frac{\pi}{3}</math>.
-::<span class="exam">b) The curve
+<span class="exam">b) The curve
 ::::::<math>y=1-x^2,~~~0\leq x \leq 1</math>
-::<span class="exam">is rotated about the <math>y</math>-axis. Find the area of the resulting surface.
+<span class="exam">is rotated about the <math>y</math>-axis. Find the area of the resulting surface.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"