(Solved): Three regions are defined in the figure. The \( x y \) coordinate plane is given. A rectangle conta ...

Three regions are defined in the figure. The \( x y \) 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 \( B \) \( (1,3) \), and point \( C(0,3) \). - The line \( y=3 x \) begins at the origin, goes up and right, and ends at point \( B(1,3) \). - The curve \( y=3 \sqrt[4]{x} \) begins at the origin, goes up and right becoming less steep, and ends at point \( B(1,3) \). - Region \( R_{1} \) is below the line, above the \( x \)-axis and left of the line segment \( A B \). - Region \( R_{2} \) is above the curve, right of the \( y \)-axis and below the line segment \( B C \). - Region \( R_{3} \) is below the curve and above the line. Find the volume generated by rotating the given region about the specified line. \( x_{1} \) about \( O A \)