Difference between revisions of "009B Sample Final 1, Problem 7"
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| − | + | <span class="exam">a) Find the length of the curve | |
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::::::<math>y=\ln (\cos x),~~~0\leq x \leq \frac{\pi}{3}</math>. | ::::::<math>y=\ln (\cos x),~~~0\leq x \leq \frac{\pi}{3}</math>. | ||
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| + | <span class="exam">b) The curve | ||
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::::::<math>y=1-x^2,~~~0\leq x \leq 1</math> | ::::::<math>y=1-x^2,~~~0\leq x \leq 1</math> | ||
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| + | <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;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
Revision as of 21:07, 1 February 2016
a) Find the length of the curve
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=\ln (\cos x),~~~0\leq x \leq \frac{\pi}{3}} .
b) The curve
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=1-x^2,~~~0\leq x \leq 1}
is rotated about the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} -axis. Find the area of the resulting surface.
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Solution:
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(b)
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(c)
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