Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about the specified axis. y = x3, y = 8, x = 0; about x = 3

See the image for a representative cylindrical shell. The total volume of the solid of revolution is the sum of an infinite number of such infinitesimally thin shells. Each shell has a surface area determined exactly by the value of , with radius and height . We have ranging from 0 to 2, since .

So the volume is given by the integral

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )

step-by-step explanation: