Final answer:
To find the volume of the solid formed by revolving the region y = 49 - x² about the y-axis, we can use the method of cylindrical shells.
Step-by-step explanation:
To evaluate the definite integral that represents the volume of the solid formed by revolving the region about the y-axis, we can use the method of cylindrical shells.
The region is given by the equation y = 49 - x². To find the limits of integration, we need to solve for x in terms of y: x = ±√(49 - y).
The volume of the solid can be found using the formula V = ∫(2πx)(y)dy, where the limits of integration are from y = 0 to y = 49.