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 shaded area can be found by calculating the definite integral of the function between the limits of integration. The limits of integration are the x-values where the function intersects the x-axis. From the graph, we can see that the function intersects the x-axis at x=0 and x=3. So, we need to calculate the definite integral of the function between 0 and 3.

∫(6-x)dx between 0 and 3
= [(6-3)^2/2] - [(6-0)^2/2]
= (9/2) - (18/2)
= -4.5

Since the area cannot be negative, we take the absolute value and get:
|Area| = 4.5

Thus, the shaded area is 4.5 square units, which is closest to option B.

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