Final answer:
To find the volume of the region in the first quadrant bounded by x=0, y=0, x=1 and y=x²+1 when revolved about the x-axis, use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the region in the first quadrant bounded by x=0, y=0, x=1 and y=x²+1 when revolved about the x-axis, we can use the method of cylindrical shells.
The volume of a cylindrical shell is given by the formula V = 2πrhΔx, where h is the height of the shell (given by y), r is the distance from the axis of rotation to the shell (given by x), and Δx is the thickness of the shell.
Integrating this formula from x=0 to x=1, we get:
V = ∫(2πx)(x²+1)dx
Simplifying and evaluating the integral, we find that the volume is:
V = π/3 + π/2 = 5π/6