Math 152 AU10 Exam 2 Review Solutions

# Math 152 AU10 Exam 2 Review Solutions - MSLC Math 152...

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MSLC Math 152 Midterm 2 Review Solutions Disclaimer: This review should NOT be used as your only guide for what to study. 1) Evaluate the following integrals a. 2 22 22 4 2 1 2 2 2 22 1 2 4444 4 1 4 2 2 14 11 1 ln( ) arctan( ) ln( 4) arctan 24 1 2 2 2 x xx x dx dx dx dx dx xxxx x ux v du xdx dv dx du x dv u v c x c uv          b. (2 1) 1 2 1) 1) 1 1 2 2 1) 21 2 x w w w ww w w x x xe d x wx dw dx we du uw ve du dw dv e dw we e du we e c x e e c    c. 23 2 4 35 3 5 1 2 s i n( 2)c o s( 2) cos (2 ) 1 sin (2 ) s in(2) ( 1 s )co s (2) ( s in(2) s s sin(2 ) 2cos(2 ) sin (2 ) sin (2 ) () 3 5 d x x d x x d x du x dx uu x x d u c c

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d. 5 5 22 2 4 35 3 5 24 3 sin (3 ) 3 sin ( ) sin ( ) 1 cos ( ) (1 cos ( )) sin( ) 2cos ( ) cos ( ))sin( ) cos( ) sin( ) c o s ( ) c o s ( ) 2 ) cos( ) 3 5 2cos (3 ) cos(3 ) 3 xdx ux du dx udu uu u u du u u u du wu dw u du ww u u d w w c u c x x     5 cos (3 ) 5 x c e. 2 1 12 11 1 ln( ) ln( ) ln( ) ln( ) ln 1 ln( ) x dx x v x du x dx dv x dx x xx x d x x d x x x c c x    f.  2 2 2 9 3sin( ) 3cos( ) 99 s i n () 3 s i n 3 s i n cos ( ) 1 sin ( ) 3 3 3 csc sin sin( ) sin( ) 3ln csc cot 3cos 0 sin 3 9 39 3ln x dx x x dx d dd d c c x h ax x  2 2 93 9 33 l n 9 3 x cx c 
g.  21 33 55 22 3 3 3 3 3 3 1 1 11 (1 ) ) x dx x ux du dx uu du du u u du u x x cc         h. 2 16 16 99 2 1 1 3 91 6 9(1 ) ) 4 3 4 3 13 1 1 1 4 arcsin( ) arcsin 34 4 4 3 ) xx dx dx dx x x u du dx x du u c c u   i.  sin(3 )sin(2 ) 1 sin( )sin( ) cos( ) cos( ) 2 1 cos(3 2 ) cos(3 2 ) 2 1 cos( ) cos(5 ) sin( ) sin(5 ) 5 d x AB A B A B d x x xd x x x c   

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j. 1 2 11 22 2 1 2 2 2 2 2 2 2 1 2 arcsin( ) arcsin( ) 1 arcsin( ) 1 (1 ) 1 arcsin( ) ) ) arcsin( ) ) ) sin cos xx d x ux v x dx du dv xdx x dx x x v x xdx du dx dv x x x x d x xxx x x d x x dx d       1 2 1 2 1 2 1 2 2 1 2 2 1 2 1 4 1 1 4 2 1 4 arcsin( ) ) sin ) cos arcsin( ) ) cos arcsin( ) ) cos(2 )) arcsin( ) ) ( sin(2 )) arcsin( ) ) ( x d x d x d x c x   1 2 2 2 1 4 2 1 1 4 4 1 24 4 arcsin sin cos ) sin 1 1 1 arcsin( ) ) (arcsin ) 1 arcsin( ) 1 arcsin 1 arcsin 1 x c xo x h ax x x x c x x c x x c   (Hard!)
k.

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## This note was uploaded on 11/28/2011 for the course CHEM 121 taught by Professor Wyzlouzil during the Spring '07 term at Ohio State.

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Math 152 AU10 Exam 2 Review Solutions - MSLC Math 152...

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