Mth252intskillsv2key

Mth252intskillsv2key - Mth 252 Integration Skills Test...

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Mth 252 Integration Skills Test Version 2 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. 3 x + 2 ( ) 2 dx ! = 3( x + 2) ! 2 dx " = ! x + 2) ! 1 + C or ! 3 x + 2 + C 2. 1 + x x dx ! = x ! 1 2 + 1 dx " = 2 x 1 2 + x + C or 2 x + x + C OR 1 + x x dx ! = 2 u du ! = u 2 + C = 1 + x ( ) 2 + C u = 1 + x du = dx 2 x 3. ! sin 5 + 2 ( ) " d = 1 2 sin( u ) du ! = " 1 2 cos( u ) + C = " 1 2 cos 5 + # 2 ( ) + C u = 5 + 2 du = 2 d 4. sec 2 (3 x ) dx ! = 1 3 sec 2 u du ! = 1 3 tan u + C = 1 3 tan(3 x ) + C u = 3 x du = 3 dx
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Mth 252 Integration Skills Test Page 2 Scarborough Version 2 5. sin 2 (3 ! ) d " = 1 2 ! 1 2 cos(6 " ) d = 1 2 ! 1 12 sin(6 ) + C # OR sin 2 (3 ) d " = # 1 3 sin(3 )cos(3 ) + cos 2 (3 ) d " = # 1 3 sin(3 )cos(3 ) + 1 # sin 2 (3 ) d " u = sin(3 ) dv = sin(3 ) d du = 3cos(3 ) v = # 1 3 cos(3 ) 2 sin 2 (3 ) d " = # 1 3 sin(3 )cos(3 ) + 1 d " = # 1 3 sin(3 )cos(3 ) + Then sin 2 (3 ) d " = 1 2 # 1 6 sin(3 )cos(3 ) + C 6. dx x 2 + 4 x + 4 ! = dx ( x + 2) 2 = ( x + 2) ! 2 dx " = ! ( x + 2) ! 1 + C or ! 1 x + 2 " + C 7. x 2 ! 1 x " dx = tan sec sec tan d " = tan 2 d " = sec 2 # 1 d " = tan # + C = x 2 # 1 # sec # 1 x + C x = sec dx = sec tan d x 2 " 1 = tan
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Mth 252 Integration Skills Test
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Mth252intskillsv2key - Mth 252 Integration Skills Test...

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