A new worker on an assembly line can do a particular task in such a way hat if y units are completed per day after t days on the assembly line, then = k (90 - y) where k is a positive constant and y < 90 for all values t 0 On the day the worker starts, 60 units are completed and on the 5th day, the worker completes 75 units. Express y as a function t. How many units does the worker complete on the 9th day? How many units does the worker complete on the 29th day? How many units can the worker eventually be expected to complete? How long will the worker complete 80 units? II. Integrate the following 1. Ans. 2. Ans. 3. Ans. 4. Ans. 5. Ans. 6. 7. Ans. 8. Ans. 9. Ans. 10. Ans. 11. Ans. 12. Ans. 13. 14. 15. 16. 17. II. Integrate by Parts 1. Ans. x sin x + cos x + C 2. Ans. ex(x 1) + C – 3. Ans. x3( 3 lnx 1) + C – 4. 5. 6. Ans. cos x + 2x sin x + 2 cos x+ C –x2 7. Ans. e-3x (9x2 + 6x + 2) + C 8. Ans. 9. Ans. x [sin( lnx) cos( lnx)] + C – 10. Ans. e2x ( 3sin 3x + 2cos 3x) + C 11. Ans. ( csc x cot x ln) + C – 12. 15. 13. 16. 14. 17. III. Integrate by partial Fractions 1. Ans.
A new worker on an assembly line can do a particular task in such a way hat if y units are completed per day after t days on the assembly line, then = k (90 - y) where k is a positive constant and y < 90 for all values t 0 On the day the worker starts, 60 units are completed and on the 5th day, the worker completes 75 units. Express y as a function t. How many units does the worker complete on the 9th day? How many units does the worker complete on the 29th day? How many units can the worker eventually be expected to complete? How long will the worker complete 80 units? II. Integrate the following 1. Ans. 2. Ans. 3. Ans. 4. Ans. 5. Ans. 6. 7. Ans. 8. Ans. 9. Ans. 10. Ans. 11. Ans. 12. Ans. 13. 14. 15. 16. 17. II. Integrate by Parts 1. Ans. x sin x + cos x + C 2. Ans. ex(x – 1) + C 3. Ans. x3( 3 lnx – 1) + C 4. 5. 6. Ans. –x2 cos x + 2x sin x + 2 cos x+ C 7. Ans. e-3x (9x2 + 6x + 2) + C 8. Ans. 9. Ans. x [sin( lnx) – cos( lnx)] + C 10. Ans. e2x ( 3sin 3x + 2cos 3x) + C 11. Ans. ( csc x cot x – ln) + C 12. 15. 13. 16. 14. 17. III. Integrate by partial Fractions 1. Ans.
intecal_practice_exercises_4.docx