Volumes with cross sections: squares and rectangles (intro)

Let $f(x)=5-x$f, left parenthesis, x, right parenthesis, equals, 5, minus, x and $g(x)=2\cdot \text{sin}\left(\dfrac{\pi x}{6}\right)$g, left parenthesis, x, right parenthesis, equals, 2, dot, start text, s, i, n, end text, left parenthesis, start fraction, pi, x, divided by, 6, end fraction, right parenthesis. Let $R$R be the region enclosed by the graphs of $f$f and $g$g and the $y$y-axis.

Region $R$R is the base of a solid. For each $x$x-value, the cross section of the solid taken perpendicular to the $x$x-axis is a rectangle whose base lies in $R$R and whose height is $2x$2, x.