MATH SOLVE

3 months ago

Q:
# 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 = 9

Accepted Solution

A:

Answer:200π cubic units.Step-by-step explanation:Use the general method of integrating the area of the surface generated by an arbitrary cross section of the region taken parallel to the axis of revolution.Here the axis x = 9 is parallel to the y-axis.The height of one cylindrical shell = 8 - x^3. The radius = 9 - x. 2The volume generated = 2π∫ (8 - x^3) (9 - x) dx 0= 2π ∫ ( 72 - 8x - 9x^3 + x^4) dx 2= 2 π [ 72x - 4x^2 - 9x^4/4 + x^5 / 4 ] 0= 2 π ( 144 - 16 - 144/4 + 32/4)= 2 π * 100= 200π.