Mth252intskillsv1key

Mth252intskillsv1key - x + 1) + C 7. x 5 + x 2 ! dx = 1 2 u...

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Mth 252 Integration Skills Test Version 1 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 dx ! = 3 u du ! = 3ln u + C = 3ln x + 2 + C u = x + 2 du = dx 2. xe ! x 2 dx " = ! 1 2 e u du = ! 1 2 " e u + C = ! 1 2 e ! x 2 + C u = ! x 2 du = ! 2 xdx 3. dx 5 x ! = 1 5 x ! 1/2 dx = 2 5 " x + C 4. sec(3 x ) dx ! = 1 3 sec( u ) du = ! 1 3 ln sec( u ) + tan( u ) + C = 1 3 ln sec(3 x ) + tan(3 x ) + C u = 3 x du = 3 dx
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Mth 252 Integration Skills Test Page 2 Scarborough Version 1 5. sin 4 ( ! )cos( ) d " = u 4 du ! = 1 5 u 5 + C = 1 5 sin 4 ( " ) + C u = sin( ) du = cos( ) d 6. dx x 2 + 2 x + 2 ! = dx ( x + 1) 2 + 1 = du u 2 + 1 ! ! = tan " 1 u + C = tan " 1 (
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Unformatted text preview: x + 1) + C 7. x 5 + x 2 ! dx = 1 2 u ! 1/2 du = u + C = 5 + x 2 + C " u = 5 + x 2 du = 2 xdx 8. x sin(2 x ) dx ! = ! 1 2 x cos(2 x ) + 1 2 cos(2 x ) dx " = ! 1 2 x cos(2 x ) + 1 4 sin(2 x ) + C u = x dv = sin(2 x ) dx du = dx v = ! 1 2 cos(2 x ) 9. 5 x + 5 ( x ! 1)( x + 4) dx " = 2 x ! 1 + 3 x + 4 dx " = 2ln x ! 1 + 3ln x + 4 + C 5 x + 5 ( x ! 1)( x + 4) = A x ! 1 + B x + 4 A ( x + 4) + B ( x ! 1) = 5 x + 5 Let x = ! 4 " ! 5 B = ! 15 " B = 3 Let x = 1 " 5 A = 10 " A = 2 10. tan(5 ) d " = 1 5 tan u du ! = 1 5 ln sec u + C = 1 5 ln sec(5 ) + C u = 5 du = 5 d...
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Mth252intskillsv1key - x + 1) + C 7. x 5 + x 2 ! dx = 1 2 u...

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