The function f is defined by `f(x)=(180)/(x+3)` for `x ge 0`, and `f(x) = 60` for `x lt 0`. Figure shows the graph of `y = f(x)`. What is the sum of the areas of the three shaded rectangles ?

Options

A. 111
B. 135
C. 141
D. 180

Answer

C

Explanation

The vertial dimension of the shaded rectangle whose horizontal dimension is on the x - axis for `3 le x le 6` is `f(6)=(180)/(6+3)=(180)/(9)=20`. The area of this shaded rectangle is `20(3)=60`.
The vertical dimension of the shaded rectangle whose horizontal dimension is on the x - axis for `6 le x le 9` is `f(9)=(180)/(9+3)=(180)/(12)=15`. The area of this shaded rectangle is `15(3)=45`.
The vertical dimension of the shaded rectangle whose horizontal dimension is on the x - axis for `9 le x le 12` is `f(12)=(180)/(12+3)=(180)/(15)=12`. The area of this shaded rectangle is `12(3)=36`.
The sum of the areas of the three shaded rectangles is `60+45+36=141`.