Question

use a geometric formula to find the area between the graphs of ( y = f(x) ) and ( y = g(x) ) over the indicated interval.

( f(x)=54 ),
( g(x)=39 ;2,12 )

the area is (square) square units.

Explanation:

Step1: Determine the height of the rectangle

The height \(h\) of the rectangle formed between the two horizontal lines \(y = f(x)=54\) and \(y = g(x) = 39\) is \(h=f(x)-g(x)\).
\(h=54 - 39=15\)

Step2: Determine the width of the rectangle

The width \(w\) of the rectangle over the interval \([a,b]=[2,12]\) is given by \(w=b - a\).
\(w=12-2 = 10\)

Step3: Calculate the area of the rectangle

The area \(A\) of a rectangle is \(A=h\times w\).
\(A=15\times10=150\)

Answer:

150