22sp09-ex2-practice3-solutions

22sp09-ex2-practice3-solutions - a h ig9a ieE a# e i a h99...

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Unformatted text preview: a h ig9a ieE a# e i a h99 h e b e h iea e eak e f ea ie ea h ea e iad f h e k b e i i ed ed g i ea id ea fh ed i e e ead age f b e ha h d e eee ed4 :ea e e ide e a i h e ab f h ieaY h d a e ifag i e e f b e i h i a h e a ieea ha i d b e eah e ab f h eea ie i : 88995ad 5 f e bk F id h e eg h fh e e y = ln(cos( x )) x [0 ,/ 4] i i Length = integraldisplay / 4 radicalBigg 1 + parenleftbigg- sin x cos x parenrightbigg 2 dx = integraldisplay / 4 radicalbig 1 + tan 2 xdx = integraldisplay / 4 sec xdx = ln | sec x + tan x || / 4 = ln( 2 + 1) . F id h ea ea fh e fae fe ib a i edb a ig h e e y = sin x x [0 , ] a d h e x a i i ieh e faea ea fag ah e eda daa i i integraltext 2 rds h e SA = integraldisplay 2 rds = integraldisplay 2 y radicalBigg 1 + parenleftbigg dy dx parenrightbigg 2 dx = integraldisplay 2 sin( x ) radicalBig 1 + (cos( x )) 2 dx e u = cos( x ) , =- integraldisplay 1 1 2 radicalBig 1 + ( u ) 2 du e u = tan( ) =- integraldisplay 4 4 2 sec( ) sec 2 ( ) d = integraldisplay 4 4 2 sec 3 ( ) d = 2 bracketleftBigg sec( ) tan( ) | 4 4- integraldisplay 4 4 tan 2 ( ) sec( ) d bracketrightBigg = 2 bracketleftBigg sec( ) tan( ) | 4 4- integraldisplay 4 4 ( sec 2 ( )- 1 ) sec( ) d bracketrightBigg = 2 bracketleftBigg sec( ) tan( ) | 4 4- integraldisplay 4 4 sec 3 ( ) d + integraldisplay 4 4 sec( ) d bracketrightBigg . eh e integraltext 4 4 sec 3 ( ) d f h e a i e h e e i i eadd i id e b 2 integraldisplay 4 4 sec 3 ( ) d = 2 bracketleftBigg sec( ) tan( ) | 4 4- integraldisplay 4 4 sec 3 ( ) d + integraldisplay 4 4 sec( ) d bracketrightBigg 4 integraldisplay 4 4 sec 3 ( ) d = 2 bracketleftBigg sec( ) tan( ) | 4 4 + integraldisplay 4 4 sec( ) d bracketrightBigg 2 integraldisplay...
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This note was uploaded on 11/06/2009 for the course MATH 22 taught by Professor Dodson during the Spring '05 term at Lehigh University .

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22sp09-ex2-practice3-solutions - a h ig9a ieE a# e i a h99...

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