Question

9) Set up the integrals but do not evaluate. Provide graphs. a. Of the area of the region outside ofr = 3sine and inside r = 2 - sine.Shade the region and show how you found the limits of integration. Show them on the graph. b. Of the surface of the solid by rotating the region given by y = /5-xon (1,2) and (5,0) about the x- axis, both explicitly and implicitly Explicitly: Implicitly

Answer 1

ANSWER:

C 9. g) Qiven, 8=3 sinco) 8=2-sin(o) 8=3 sino = 2-sinco) =) sino=1 2 50 O=T 6 3 r=3sino 16 T16 Area is symmetric about y-axis 18=2-sino -3 For OE [ 31 1 , 2n 8=2-sino OE[0,1/6]; rin= 3 sino rout = 2-sino TT T16 Area = 2 0 3/2 [J "[143sines?+ (2_sing)? 3 do +5 12-sino)do] do T16 - (2-Sino)? do TIG q sindo do L-T/2. 0

2 311 25 11 2 (10) b) Y = 15-4 (1,2) to 15,0) X = 5-y? about x-anis y (1,2) 2 X 5 dy dx ds = { 1 + ( 27 ) z dx 2/5 dx 415-X) dx 21-4X 4(5-) surface Area = 21 2T y ds тјуа. 5 = 21 √5-X 21-ux 2/5 dx

3 121-4x dx dx dy 19 - 2y ; ds. (it (dr) z dy = /1+4y2 dy - Syd surface Area = 211 27 yds 2 2T TJ7/1-+уу?- dy 6 2 for 21T y/1+442 dy