(Solved): Three regions are defined in the figure. Find the volume generated by rotating the given region avo ...

Three regions are defined in the figure. Find the volume generated by rotating the given region avout tne specified line. $$R_1\text{ about }OA$$ Three regions are defined in the figure. The $$xy$$ coordinate plane is given. A rectangle containing a line, a curve, and three shaded regions is on the graph. - The rectangle is formed by the origin, point $$A(1,0)$$, point $$B$$ $$(1,2)$$, and point $$C(0,2)$$. - The line $$y=2x$$ begins at the origin, goes up and right, and ends at point $$B(1,2)$$. - The curve $$y=2\sqrt{x}$$ begins at the origin, goes up and right becoming less steep, and ends at point $$B(1,2)$$. - Region $$R_1$$ is below the line, above the $$x$$-axis and left of the line segment $$AB$$. - Region $$R_2$$ is above the curve, right of the $$y$$-axis and below the line segment $$BC$$. - Region $$R_3$$ is below the curve and above the line. Find the volume generated by rotating the given region about the specified line. $$R_1$$ about $$OA$$