P442: 1, 2, 5, 6(SECTION 6.1)

P490–491: 7 –27ODD(SECTION 7.1)4 attachmentsSlide 1 of 4

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1-4 Find the area of the shaded region. 1. YA 2. YA 10. y = sin x, y = 2x, 11. x= 1 – y? x=) 12. 4x + y2 = 12, x = y=x (1, e) x = 8 y=e” ((1,1) omputers, and Devices y=xe” 0 0 sts y=1/x Calculus nd Models 3. YA 4. YA Derivatives x=y? – 4y on Rules x=y² – 2 y=1 (-3, 3) s of x x=e s of Integration 13-28 Sketch the region its area. 13. y = 12 – x?, y = 14. y = x, y = 4x – 15. y = sec x, y = 8c 16. y = cos x, y = 2 – 17. r= 2y?, x= 4 +) 18. y = 1x – 1, X- = cos TX, y = 4. 20. x = y, y= V2 – 21. y = tan x, y = 2 sir 22. y = r, y = x 23. y = x/2x, y = 5x? 24. y = cos x, y = 1 – 25. y = x4, y = 2 – |x| y=-1 х of Integration x=2y – y2 19. y blications of Equations ic Equations and nates equences and and the Space 5-12 Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approxi- mating rectangle and label its height and width. Then find the area of the region. 5. y = e’, y = x² – 1, x= -1, x = 1 6. y = sin x, y = x, x= 1/2, x= Junctions erivatives 26. v= sinh r v== 6.1 EXERCISES 1-4 Find the area of the shaded region. y = 2 2. 10. y = sin x, 11. x = 1 – y2, 12. 4x + y² = 12, X = y= (1, e) x=8 y=et ter 13-28 Sketch the regic its area. 0 X 0 ur y=1/x 3. YA 4. YA x = y? – 4y x=y? – 2 y=1 1 (-3, 3) 13. y = 12 – x, y 14. y = x?, y = 4x 15. y = secʻx, y = & 16. y = cos x, y = 2 I 17. x = 2y?, x= 4 + 18. y = (x – 1, x – X y=-1 XE = 2y – y? 19. y = cos TX, у — 20. x = y^, y = 2 21. y = tan x, y = 2 5-12 Sketch the region enclosed by the given curves. Decide 22. y = V = X ILS alca. y=1/x 3. VA 4. x = y2 – 4y x=y? – 2 y=1 (-3, 3) x= e y=-1 x= 2y = y2 13. y = 12 – x² 14. y=x?, y = 4x 15. y = secʻx, y = 8 16. y = cos x, y = 2 17. x= 2y2, x= 4 + 18. y = (x – 1, x – 19. y = COS TX, y 20. r= y4, y = 12 21. y = tan x, y = 2 22. y = x, y = x 23. y = 2x, y = 5 24. y = cos x, y = 1 25. y = x^, y= 2 – 26. y = sinh x, y= 27. y = 1/x, y = x, 28. y = 1x, y = 2x 5–12 Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approxi- mating rectangle and label its height and width. Then find the area of the region. 5. y = e, y = x² – 1, x=-1, x= 1 6. y = sin x, y = x, x= 1/2 x= 7. y = (x – 2), y = x 8. y = x2 – 4x, y = 2x 9. y = 1/x, y= 1/x”, x= 2 Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third p 7.1 EXERCISES 1-2 Evaluate the integral using integration by parts with the indicated choices of u and dv. 1. dx;u= x, dv = e2x dx 16. dz – S xe 2. | Va In x dx; u = lnx, dv = V« dx 13. ſt cscºt dt 15. (In x)?dx ſe20 19. Sz*e* dz 17. sin 30 de 20 de 3-36 Evaluate the integral. 14. x cosh ax dx Sio 18. Se Seco 20. x tan’x dx 22. S (arcsin x)? dx 24. [‘(x? + 1)e* dx \$ w? In w dw *** ? sin 2t dit 21. ) xe 2x (1 + 2x) dx 23. X COS TTX dx 3. x cos 5x dx 5. S te- dit 7. S (x2 + 2x) cos x dx 9. I cos ‘x dx 11. St*In t dt 4. yeo2y dy 6. S (x – 1) sin ax dx · St sin Bt dt 10. ſ In Vå dx 12. 5 tan! 2y dy 8. 26. So? 25. y sinh ydy so 29. (” x sin x cos x dx I 27. ps In R dR R2 28. T 30. arctan(1/x) dx

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