Question

3. Use the shell method to find the volume of the solid generated by the region bounded by y = { +1, y = -x + 4, and x = 4 about the y-axis.

Answer 1

I have done it for you in detail. Kindly go through.

Bounding Curvel: y = x + x= 4 +1 ) y = -x+4 modating about about y-axis. R(x) is the distance x=4 5 between axis of revolution and center of rectangle. H(x) is the height of the rectangle e+ y = 2 V R(x) =X -3 > 2 5 y=-X+4 2 Here H60) le + ) - (-x+4) and R(x) = x 1 11 3+1+X-4 3x - 3 3x - 3 a=2 and b= 4

b 27 R () H(a) dx a 4 21 XC Six-3) da 2 4 271 2 4 $(3x -3x) dx 21 () - 251 - Sape. *** *(4- 48 - 8412) 20 T So Volume of obtained surface is 2on cubic units