Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the y-axis. y = x2/3 The x y-coordinate plane is given. A curve, a shaded region, a rectangle, and an arrow indicating the axis of rotation are on the graph.
The curve starts at the origin, goes up and right becoming less steep, and stops at the point (1, 1).
The shaded region is right of the y-axis and left of the curve from y = 0 to y = 1.
The approximating rectangle occurs at y = 0.5, extends horizontally right from the y-axis to the curve, and has width Δy.
The arrow rotates around the y-axis.