Please #31, 37, 41, 45, 53, 63, 65, 71

5-8 Find the area of the shaded region. 29-34 Find the area of the region that lies inside both curves. 29.r=35in0. r=3cosfl 30.r=l+cos. r=lc056 31.r=sin23. r=00529 32.r=3+2cos. r=3+25in6 33. l=2sin20. r=l v r=sm26 r=2+cost9 34.r=asin. r=bcos, a>0,b>0 7. 8. 35. Find the area inside the larger loop and outside the smaller loop of the limacon r = % + cos 9. 36. Find the area between a large loop and the enclosed small w loop of the curve r = 1 + 2 cos 3H. r = 4 + 3 sin r = V51" 3' I g 6'5. 217 37-42 Find all points of intersection of the given curves. 37. r= sin. r= l - sin 9-12 Sketch the curve and nd the area that it encloses. 38. r = l + cos 0. r = l sin 9.r=4cos 10. r=2+2cos 39.r=25in28. r=t 11. r= 325in9 12. r=25in38 40.r= cost), r=sin26 E 13-16 Graph the curve and nd the area that it encloses. 41- r"' = 2 COS 23. 1' = l 13. r = 2 + sin 48 14. r 2cos 46 42. r" = sin 29' r" = cos 23 15. r= I + cosz(53) 16. r= l + 55in 69 43-46 Find the area of the shaded region. 17-21 Find the area of the region enclosed by one loop of 43. ,- = 3 + 2 cos a the curve. 17. r = 4cos 30 18. r1 = 4 cos 20 19. r = sin 40 20. r = 2 sin 50 \I I' 21. r= l + 25in6 (inner loop) 22. Find the area enclosed by the loop of the strophoid r = 2 cost] - sec. 23-28 Find the area of the region that lies inside the rst curve and outside the second curve. 23. r=4sin6, r=2 24.r=l-sin9. r=l 25. r"=8cosZB, r=2 26.r=l+oos. r=2-cos 27. r=3cos6. r=l +cos 28. r= 35in6. r= 2 - sine 45. r= 1+ cos 0 53-54 Find the exact length of the portion of the curve shown in blue. 53. r = 3 + 3 sin 0 r = 3 cos 0 46. r =1 - 2 sin 0 54. r = 0+2 55-56 Find the exact length of the curve. Use a graph to 47. The points of intersection of the cardioid r = 1 + sin0 and determine the parameter interval. the spiral loop r = 20, -TT/2