From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x.

Question

For example A(4)=12 is the area of the 4 by 3 rectangle. (a) Evaluate A(2.5) (b) Evaluate A(4) - A(1)

Answer 1

A(4)=12, so we can write A(x)=3x because the rectangle is bound by y=3.

A(2.5)=7.5; A(4)-A(1)=12-3=9.

 

A(4) is the rectangle formed by the blue line, red line and the axes.

A(2.5) is the rectangle formed by the green line, red line and the axes.

A(1) is the rectangle formed by the pink line, red line and the axes.

A(4)-A(1) is the rectangle formed by the blue line, red line and the pink line and x axis.