Mth252intskillsv3key

Mth252intskillsv3key - = 1 3 e 3 x 9. x 2 x + 1 dx ! = x !...

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Mth 252 Integration Skills Test Version 3 NAME (print)_____ KEY _____________________ Scarborough Recitation Time (Circle One) NAME (sign) _______________________________ 12:00 2:00 4:00 Student Number _____________________________ TIME LIMIT 30 Minutes NO CALCULATORS OR NOTES ALLOWED You must show your work to receive credit. Compute the following integrals: Use the back of the pages if you need more room. Circle your final answer. 1. x + x 2 dx ! = 1 2 x 2 + 1 3 x 3 + C 2. 5 1 + 5 x dx ! = du u = ln u + C = ln 1 + 5 x + C ! u = 1 + 5 x du = 5 dx 3. ln( x ) ! dx = x ln( x ) ! 1 x " x dx = x ln( x ) ! dx " = x ln( x ) ! x + C u = ln( x ) dv = dx du = 1 x dx v = x 4. x 2 e ! x 3 dx " = ! 1 3 e u du " = ! 1 3 e u + C = ! 1 3 e ! x 3 + C u = ! x 3 du = ! 3 x 2 dx
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Mth 252 Integration Skills Test Page 2 Scarborough Version 3 KEY 5. tan(3 ! ) d " = 1 3 tan( u ) du ! = 1 3 ln sec( u ) + C = 1 3 ln sec(3 " ) + C u = 3 du = 3 d OR tan(3 ) d " = 1 3 tan( u ) du ! = " 1 3 ln cos( u ) + C = " 1 3 ln cos(3 # ) + C u = 3 du = 3 d 6. dx x 2 + 4 x + 5 ! = dx x 2 + 4 x + 4 + 1 = dx ( x + 2) 2 + 1 = du u 2 + 1 = arctan( u ) + C = arctan( x + 2) + C ! ! ! u = x + 2 du = dx 7. 1 x ( x + 2) ! dx = 1 2 ( ) x ! " 1 2 ( ) x + 2 dx = 1 2 ln x " 1 2 ln x + 2 + C 1 x ( x + 2) = A x + B x + 2 A ( x + 2) + Bx = 1 Let x = 0 ! 2 A = 1 ! A = 1 2 Let x = " 2 ! " 2 B = 1 ! B = " 1 2 NOTE: 1 2 ln x ! 1 2 ln x + 2 + C = 1 2 ln x x + 2 + C
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Mth 252 Integration Skills Test Page 3 Scarborough Version 3 KEY 8. xe 3 x dx ! = 1 3 xe 3 x ! 1 3 e 3 x dx " = 1 3 xe 3 x ! 1 9 e 3 x + C u = x du = e 3 x dx du = dx u
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Unformatted text preview: = 1 3 e 3 x 9. x 2 x + 1 dx ! = x ! 1 + 1 x + 1 dx " = 1 2 x 2 ! x + ln x + 1 + C x + 1 x 2 + x + x ! 1 x 2 + x ! x ! x ! 1 1 OR x 2 x + 1 dx ! = x 2 ! 1 + 1 x + 1 dx = ( x ! 1)( x + 1) x + 1 + 1 x + 1 dx " = x ! 1 + 1 x + 1 dx = 1 2 x 2 ! x + ln x + 1 + C " " OR x 2 x + 1 dx ! = ( u ! 1) 2 u du = u 2 ! 2 u + 1 u du = u ! 2 + 1 u du = " " " 1 2 u 2 ! 2 u + ln u + C u = x + 1 du = dx = 1 2 ( x + 1) 2 ! 2( x + 1) + ln x + 1 + C 10. cos( ! )sin( ) d " = u du ! = 1 2 u 2 + C = 1 2 sin 2 " + C u = sin( ) du = cos( ) d OR cos( )sin( ) d " = ! u du " = ! 1 2 u 2 + C = ! 1 2 cos 2 # + C u = cos( ) du = " sin( ) d OR cos( )sin( ) d " = 1 2 sin(2 ) d " = # 1 4 cos(2 ) + C...
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Mth252intskillsv3key - = 1 3 e 3 x 9. x 2 x + 1 dx ! = x !...

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