Question

2. Set up (don't evaluate) the following volume integrals, for the region bounded by the given curves and revolved about the given line. Be sure to use only the disc/washer method for these. (a) region: above the x-axis, bounded by (b) region: bounded by y=x? x=2 x? + -=1 ; revolved about the x-axis and y=x ; revolved about the x-axis. 4 , x=1 (c) region: bounded by y=v2+x? , the x-axis, x=1 and x=2 ; revolved about the line y = -1. (d) region: bounded by y=vx , x=0, y=1 ; revolved about the y-axis (e) region: bounded by y=vx , x=0, y=1 ; revolved about the line x = 5 (1) region: bounded by y=vx , x=0, y=1 ; revolved about the line x = -5

Answer 1

2 Q x + 1 2 3 El above the n-anis 4710 1 2 cross section a perpendicular disc with thickness da. 2 volume - s're -lo 2 y alan q ure ( (1-x²) du y = a (rrug y=2/1-n2 16 Yan², nal n=2 y=n cy you N2 >n -> k o 122 11 volume = 2 du (24_*) about y = -1 n-anis, hal, n=2, ya = T2+n2 yZ_n2=2 2 2 n=2 hal .ܢܲ -40-1 volume of refit (1 tuzon)" dw ENSE Salaam ri 1+252 m2 + 2th) dh = r x² +2 +252 +22) du

d revolve about yo ans yarn, nzo, ya volume r (y 2 dy ny s/n 121 >n - RJ'shd gydy o e yarn, nzo, y=1 revolved about n=5 y=rn volume R(5² (5 O n25 = r (5- y2) dy S (252 (25 – 25+10y2-yy) dy aso (loya ye dy 11 f Yarn, nao, ys! revolved about 2-5 ។ volume yol yahu Sne [57992-28]dy 7 ="{'*6*+70 427 nars