Answer
We can list the quantities in order, from smallest to largest:
$B \lt E \lt A \lt D \lt C$
Work Step by Step
The integral $\int_{a}^{b}f(x)~dx$ is equal to the area between the graph and the x-axis. An area below the x-axis is negative, while an area above the x-axis is positive.
B. $\int_{0}^{3}f(x)~dx$ is the most negative value
E. $f'(1)$ is the slope of the graph at the point $x=1$ and we can see that this value is slightly negative.
A. $\int_{0}^{8}f(x)~dx$ is equal to (all of the area above the x-axis) minus (all of the area below the x-axis).
D. $\int_{4}^{8}f(x)~dx$ is equal to most of the area above the x-axis.
C. $\int_{3}^{8}f(x)~dx$ is equal to all of the area above the x-axis.
We can list the quantities in order, from smallest to largest:
$B \lt E \lt A \lt D \lt C$
