2. Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. YA y = 5x - x , y= 0 y = 5x-x2 Set up the integral that gives the volume of the solid using the shell method. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) O A. dy O B. dx The volume is (Type an exact answer.)3. Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. y= 8(1+8x2 ) , y=0, x= 0, and x = 2 8 y= - R 1+8x2 Set up the integral that gives the volume of the solid using the shell method. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) OA. dy O B. dx The volume is (Type an exact answer.)4. Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. y = 12x, y = 12, and x = 0 12- R y = 12x X 0 Set up the integral that gives the volume of the solid using the shell method. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) O A. dy O B. dx The volume is (Type an exact answer.)5. Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. y = 169 - 13x2 , y =0, and x = 0, in the first quadrant Set up the integral that gives the volume of the solid using the shell method. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) O A. dx O B. dy The volume is (Type an exact answer.)4 . h ( w) = 12- 12x1 given , y= 12 x , y = 12 , X= 0 Now , y = 12 =) 12 = 12 21 =) 1=1 and the region is upper pont of line y= 12n So , at some point r (n ) = n, height will be hin ) = 12 ( 1-21 ) So, the integral will be , = 12 - 12x V = 271 2 ( 12 - 1 2 41 ) dre O 20 ( 12 21 - 12 412) du = 21 (2 ) The volume is5 . J = 1 169-13x2, y=0, n20 around y- arms when y= 0 13 + V 169 - 13212 = 0 = ) n = V13 So , the integral will be, V = 2 0 n V 169 - 1312 / du V13 13 - 26u V 169- 13212 Our 13 ( 169 - 13 / 2 ) 32 V13 o 338 3 The volume is 338 TT 3