{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

This preview shows pages 1–2. Sign up to view the full content.

36. The radius of a horizontal cross section is ˇ 8 w 2 w 2 w y w 2 w , where y is distance below the rim. The area is p (64 2 y 2 ), the weight is 0.04 p (64 2 y 2 ) D y , and the work to lift it over the rim is 0.04 p (64 2 y 2 )( y ) D y . The total work is E 8 2 0.04 p y (64 2 y 2 ) dy 5 0.04 p E 8 2 (64 y 2 y 3 ) dy 5 0.04 p 3 32 y 2 2 } 1 4 } y 4 4 5 36 p < 113.097 in.-lb. 37. The width of a thin horizontal strip is 2(2 y ) 5 4 y , and the force against it is 80(2 2 y )4 y D y . The total force is E 2 0 320 y (2 2 y ) dy 5 320 E 2 0 ( 2 y 2 1 2 y ) dy 5 320 3 2 } 1 3 } y 3 1 y 2 4 5 } 12 3 80 } < 426.67 lb. 38. 5.75 in. 5 } 2 4 3 8 } ft, 3.5 in. 5 } 2 7 4 } ft, and 10 in. 5 } 5 6 } ft. For the base, Force 5 57 1 } 2 4 3 8 } 3 } 2 7 4 } 3 } 5 6 } 2 < 6.6385 lb. For the front and back, Force 5 E 5/6 0 57 1 } 2 7 4 } 2 y dy 5 } 3 2 9 4 9 } 3 } 1 2 } y 2 4 < 5.7726 lb. For the sides, Force 5 E 5/6 0 57 1 } 2 4 3 8 } 2 y dy 5 } 13 4 1 8 1 } 3 } 1 2 } y 2 4 < 9.4835 lb. 39. A square’s height is y 5 ( ˇ 6 w 2 ˇ x w ) 2 , and its area is y 2 5 ( ˇ 6 w 2 ˇ x w ) 4 . The volume is E 6 0 ( ˇ 6 w 2 ˇ x w ) 4 dx , which using NINT evaluates to exactly 14.4. 40. Choose 50 cm as a conveniently large upper limit. E 50 20 } 3.4 ˇ 1 2 w p w } e 2 ( x 2 17.2) 2 /(2 ? 3.4 2 ) dx , evaluates, using NINT to < 0.2051 (20.5%). 41. Answers will vary. Find m , then use the fact that 68% of the class is within s of m to find s , and then choose a conveniently large number b and calculate E b 10 } s ˇ 1 2 w p w } e 2 ( x 2 m ) 2 /(2 s 2 ) dx . 42. Use f ( x ) 5 } ˇ 1 2 w p w } e 2 x 2 /2 . (a) E 1 2 1 f ( x ) dx evaluates, using NINT, to < 0.6827 (68.27%). (b) E 2 2 2 f ( x ) dx < 0.9545 (95.45%) (c) E 3 2 3 f ( x ) dx < 0.9973 (99.73%) 43. Because f ( x ) \$ 0 and E 2‘ f ( x ) dx 5 1 44. [ 2 1, 3] by [ 2 1, 3] A shell has radius x and height 2 x 2 } 2 x } 5 } 3 2 } x . The total volume is E 1 0 2 p ( x ) 1 } 3 2 } x 2 dx 5 p 3 x 3 4 5 p . 45. [ 2 3, 3] by [ 2 3, 3] A shell has radius x and height } 1 x } . The total volume is E 2 1/2 2 p ( x ) 1 } 1 x } 2 dx 5 E 2 1/2 2 p dx 5 3 2 p x 4 5 3 p . 46. 3 2 } p 2 } , } 3 2 p } 4 by [ 2 2, 2] A shell has radius x and height sin x . The total volume is E p 0 2 p ( x )(sin x ) dx 5 2 p 3 sin x 2 x cos x 4 5 2 p 2 . 47. [ 2 1, 4] by [ 2 4, 1] The curves intersect at x 5 1 and x 5 3. A shell has radius x and height x 2 3 2 ( x 2 2 3 x ) 5 2 x 2 1 4 x 2 3. The total volume is E 3 1 2 p ( x )( 2 x 2 1 4 x 2 3) dx 5 2 p E 3 1 ( 2 x 3 1 4 x 2 2 3 x ) dx 5 2 p 3 2 } 1 4 } x 4 1 } 4 3 } x 3 2 } 3 2 } x 2 4 5 } 16 3 p } .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern