Find the shaded area between the given function and the x-axis.
A)

Question

Find the shaded area between the given function and the x-axis. ​   ​
A) ​

Quizplus · Accepted Answer

The area between the given function and the x-axis can be divided into two parts: one is the area of a rectangle of base 2 and height 2, and the other is the area under the curve y=2-x between x=0 and x=2. The area of the rectangle is 4. The area under the curve can be calculated using the definite integral from 0 to 2:

∫(2-x)dx = [2x-x^2/2] from 0 to 2 = 2

Therefore, the total area is 4+2=6, which is represented by choice B.

Find the Shaded Area Between the Given Function and the X-Axis