Answer:
[tex]\frac{6^2-3^2}{2} =\frac{27}{2}[/tex]
(the third answer in your list of options)
Step-by-step explanation:
The area of the region between y = x, and the x axis, between x= 3 and x=6 is the area of the trapezoid shown in the attached image.
It therefore can be calculated via the area of a trapezoid:
[tex](B+b)\,H/2=(6+3)*3/2=27/2[/tex]
or doing the integral (which it seems is what they want you to do):
[tex]\int\limits^6_3 {x} \, dx =\frac{x^2}{2} ]\limits^6_3=\frac{6^2-3^2}{2} =\frac{27}{2}[/tex]
