Answer:
D) 8
Step-by-step explanation:
We are given a continuous function <em>f</em> on the closed interval [0, 2].
Where:
And we want to find the greatest possible value of:
The range restriction tells us that even if <em>f(x)</em> = 2 for all <em>x</em> in the interval [0, 2], the smallest area possible will be 4, since that is the area of the rectangle.
Then in that case, the maximum possible value of the integral must be 8. <em>f(x)</em> cannot exceed 4, and the length of the interval is two units. Thus, the greatest possible value of the integral is 8. This will only occur if <em>f(x)</em> is a horizontal line at <em>y</em> = 4 from <em>x</em> = 0 to <em>x</em> = 2.