MAT 232 WA1 - Name College ID Thomas Edison State College Calculus II(MAT-232 Section no 5.2,5.3 5.4 Semester and year Written Assignment 1 Answer all

MAT 232 WA1 - Name College ID Thomas Edison State College...

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Name: College ID: Thomas Edison State College Calculus II (MAT-232) Section no.: 5.2,5.3, 5.4 Semester and year: Written Assignment 1 Answer all assigned exercises, and show all work. Each exercise is worth 5 points. Section 5.2 2. Find the volume of the solid with cross-sectional area A ( x ). 100 10 100 0.01 10 0.01 0 10 0.01 0 10 10 0 0 10 10 0 0 0 ( ) 10 , 0 10 ( ) 10 10 0.01 , 0.01 100 10 100 10(100) 1000 1000 1000 1000 105.17 x x b x a x u u u A x e x V A x dx e dx V e dx u x du dx du dx V e du e du V e C e C V e e 6.Find the volume of a pyramid of height 160 feet that has a square base of side 300 feet. These dimensions are half those of the pyramid in example 2.1. How does the volume compare?
(0) 300, (160) 0 15 ( ) 300 8 15 ( ) 300 8 15 15 300, 8 8 8 8 15 15 8 8 15 15 3 4,800,000 f x mx b f f f x x V A x dx x dx u x du dx V u du u du u V u du V ft The volume is 1/8 of the volume of the pyramid in example 2.1. 10. A dome “twice as big” as that of exercise 9 (see text) has outline 2 120 120 x y for 120 120 x (units of feet). Find its volume. 2 2 2 2 120 120 120 2 120 0 120 2 2 2 0 3 ( ) 120 120 120 120(120 ) 120 120 120 120 120 120 120 120 (7200) 2 2 864000 b a x x x V f x dx y y y x y V y dy y V y V ft WA 1, p. 2
12. A pottery jar has circular cross sections of radius 2 4 sin x inches for 0 2 . x Sketch a picture of the jar and compute its volume. WA 1, p. 3 2 2 2 2 2 0 0 2 2 0 2 2 0 2 2 2 2 0 0 0 2 ( ) ( ) 4 sin 2 4 sin 4 sin 2 2 1 , ,2 2 2 4 sin( ) 2 2 (sin 8sin 16) 2 sin ( ) 8 sin 16 sin b a V f x dx x f x x x V dx dx x u du dx du dx V u du V u u du V u du u du du   sin(2 ) 2 2 sin(2 ) 2 2 0 sin(2 ) 2 2 2 0 2 1 cos(2 ) 1 ( ) 1 cos(2 ) 2 2 1 2 , 2 , 2 1 1 sin( ) cos( ) cos( ) 2 2 2 sin ( ) 2 2 2 8cos 16 2 2 2 8cos 16 2 2 2 2 33 U U x u u du du du u du v u dv du dv du v v dv v dv u u du u V u u x x V V 3 32 in
18. Compute the volume of the solid formed by revolving the region bounded by 2 2 , 4 y x y x about (a) the x -axis; (b) y = 4. a. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 5 3 4 2 5 2 2 4 2 2 5 3 5 2 2 4 4 4 8 16 8 16 8 16 5 3 5 8 16 5 3 5 32 64 32 5 3 o i b b o i a a r x r x V r dx r dx V x dx x dx x dx x x dx x x x dx x dx dx x C x x dx x dx C x x x V x V