22sp09-ex2-practice2-solutions

22sp09-ex2-practice2-solutions - A G9ACCEEXA#E h e b e h...

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Unformatted text preview: A G9ACCEEXA#E 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 f h ed i e e ead age f b e ha h d e e ee 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 ea h e ab f h eea ie i :88995ad 5 f e bk F id h e eg h fh e e y = x 2- 1 8 ln x x [1 , 4] i i : igh e f a f h ea eg h fag ah L = integraldisplay 4 1 radicalBigg 1 + parenleftbigg dy dx parenrightbigg 2 dx = integraldisplay 4 1 radicalBigg 1 + parenleftbigg 2 x- 1 8 x parenrightbigg 2 dx = integraldisplay 4 1 radicalBigg 1 + parenleftbigg 4 x 2- 1 2 + 1 (8 x ) 2 parenrightbigg dx. ieh e- 1 2 i h e idd e h e i ied ha a e h i ik e h e e ik h ih i eg ieha h e i id eh ea e i id eeda e fea eB e A G9ACCEEXA#E eeh ehag ig a h e eadd i h e L = integraldisplay 4 1 radicalBigg 1 + parenleftbigg 4 x 2- 1 2 + 1 (8 x ) 2 parenrightbigg dx = integraldisplay 4 1 radicalBigg parenleftbigg 4 x 2 + 1 2 + 1 (8 x ) 2 parenrightbigg dx = integraldisplay 4 1 radicalBigg parenleftbigg 2 x + 1 8 x parenrightbigg 2 dx = integraldisplay 4 1 parenleftbigg 2 x + 1 8 x parenrightbigg dx = x 2 + 1 8 ln( x ) vextendsingle vextendsingle vextendsingle vextendsingle 4 1 = parenleftbigg 16 + 1 8 ln(4) parenrightbigg- 1 = 15 + 1 8 ln(4) . F id h ee id fh eeg i i h e xy a ebd edb e b h ea ab a y = x 2 adab eb h e i e y = 2 x + 3 5 i i : h eeg ie ed f x =- 1 x = 3 b ea e h e e i e e h e x 2 = 2 x + 3 , 0 = x 2- 2 x- 3 = ( x + 1)( x- 3) ieh eeg i i e ia ie ;h eh e igh ib e h = (2 x + 3)- x 2 b ad h ik e dx. dA = hdx = ( (2 x + 3)- x 2 ) dx ih ea ea i eg adh e A G9ACCEEXA#E x d ia e fh ee id x ig i eb x = integraltext 3 1 xdA integraltext 3 1 dA = integraltext 3 1 x ( (2 x + 3)- x 2 ) dx integraltext 3 1 ((2 x + 3)- x 2 ) dx = integraltext 3 1 2 x 2 + 3 x- x 3 dx integraltext 3 1 2 x + 3- x 2 dx = 2 3 x 3 + 3 2 x 2- 1 4 x 4 vextendsingle vextendsingle 3 1 x 2 + 3 x- 1 3 x 3 vextendsingle vextendsingle 3...
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22sp09-ex2-practice2-solutions - A G9ACCEEXA#E h e b e h...

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