两条在多于两点相交的曲线之间的面积（计算器练习）

使$f(x)=2\cos\left(\dfrac{\pi x}{3}\right)$f, left parenthesis, x, right parenthesis, equals, 2, cosine, left parenthesis, start fraction, pi, x, divided by, 3, end fraction, right parenthesis，以及$g(x)=2\cdot\dfrac{8-x}{x+6}-1$g, left parenthesis, x, right parenthesis, equals, 2, dot, start fraction, 8, minus, x, divided by, x, plus, 6, end fraction, minus, 1。如图所示，设$R$R和$S$S为$f$f和$g$g的图像所构成的两个区域。