Answer
C. The value of $F(2)$ is the largest since it is the only value that is not negative.
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. Note that: $\int_{a}^{b}f(x)~dx=-\int_{b}^{a}f(x)~dx$
A. $F(0) = \int_{2}^{0}f(t)~dt = -\int_{0}^{2}f(t)~dt \lt 0$
B. $F(1) = \int_{1}^{0}f(t)~dt = -\int_{0}^{1}f(t)~dt \lt 0$
C. $F(2) = \int_{2}^{2}f(t)~dt = 0$
D. $F(3) = \int_{2}^{3}f(t)~dt \lt 0$
E. $F(4) = \int_{2}^{4}f(t)~dt \lt 0$
The value of $F(2)$ is the largest since it is the only value that is not negative.
