Not sure how to use it on graphing calculator

Question

Estimate the area between the curvesy=4.5x and y=0.75x^2. Use a graphing calculator. 

Answer 1

From y = 4.5x and y = 0.75x², write the quadratic equation 0.75x² − 4.5x + 0 = 0

which gives x equal to {-(-4.5) ± √[(-4.5)² − 4(0.75)(0)]} ÷ (2×0.75) which reduces

to {4.5 ± √20.25}/1.5.

Then x = 0 or x = 6 and the 2 curves intersect at (x,y) = (0,0) and (x,y) = (6,27).

A graphing calculator shows that y = 4.5x is above y = 0.75x² when plotted on

the x-y plane, so the area sought is obtained by the integral

∫_{(from x=0 to x=6)}[4.5x − 0.75x²]dx equal to {2.25x² − 0.25x³|_{(from x=0 to x=6)}}

or [2.25(6)² − 0.25(6)³] − [2.25(0)² − 0.25(0)³] or 27 square units.