m23 quiz #1 (with answer) - xds S b. 5 1 , 1 x x y AOR: (i)...

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MATH023 2 nd Term 2011-2012 Quiz No. 1 A. Find the lengths of the following curves: 1. 3 0 , 2 3 , 2 3 t t y t x 2. 4 0 , ) ln(sec x x y units ) 1 2 ln( sec tan 1 tan tan sec sec 1 4 0 4 0 2 dx x dx x L x x x x dx dy 3. 3 1 , 4 1 3 1 3 y y y x ( Hint: 1 + (dx/dy) 2 is a perfect square.) B. Set up an integral for the following: 1. Length of the inner loop of the limacon cos 2 1 r d d L 3 2 3 2 2 2 5 cos 4 2 ) sin 2 ( ) cos 2 1 ( 2 units units

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2. Perimeter of the petals of the rose 3 sin 2 r d d L 6 0 2 2 6 0 2 2 3 cos 9 3 sin 12 ) 3 cos 6 ( ) 3 sin 2 ( 6 3. Area of the surface generated by revolving the given curve about the indicated axis. a. 2 0 , sin 2 , cos t t y t x AOR: (i) x-axis (ii) y-axis (i) (ii) 2 0 2 0 cos 2 2 tdt
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Unformatted text preview: xds S b. 5 1 , 1 x x y AOR: (i) x = – 1 (ii) y = 5 (i) dx x x dx x x x dx x x S x dx dy 5 1 5 1 5 1 2 ) 5 4 )( 1 ( 1 5 4 ) 1 ( 2 2 1 2 1 1 ) 1 ( 2 1 2 1 or dy y y dy y y S y dy dx x y 6 2 2 6 2 2 2 4 1 2 ) 2 ( 1 2 2 1 (ii) dx x x x S 5 1 ) 5 4 )( 1 ( ) 1 5 ( or dy y y S 6 2 2 4 1 ) 5 ( 2 c. Right half of the cardioid sin 1 r AOR: 90 o-line d d r r S 2 2 3 2 2 2 2 ) sin 1 ( cos 2 2 ) cos ( cos 2...
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This note was uploaded on 12/08/2011 for the course ECON 101 taught by Professor Smith during the Spring '11 term at Adrian College.

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m23 quiz #1 (with answer) - xds S b. 5 1 , 1 x x y AOR: (i)...

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