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The velocity of a runner at different moments in time since starting a race is given by the following table.

 t in seconds 2 4 6 8 10 v(t) in m/s 1 3 5 6 6

Based on the table, which of the following is an approximation to $\int _4^8 v(t) dt$?

$18$ meters $28$ meters $30$ meters $42$ meters $44$ meters None of the above
Use the graph of the rate, $y = R(t)$, to answer the following question:

Which value is greatest?

$\int _2^8 R(t) dt$ $\int _3^9 R(t) dt$ $\sum _{k=0}^2 R(2+ k \times \Delta t)\times \Delta t$ where $\Delta t = 2$ $\sum _{k=0}^2 R(2+ k \times \Delta t)\times \Delta t$ where $\Delta t = 1$ None of the above More information is needed
The following picture illustrates a Riemann sum using $n$ terms. The dotted lines are located at $x_0$, $x_1$, etc.

Which expression from the Riemann Sum definition of the definite integral represents the green shaded region?

$\sum _{k=0}^{n-1} f(x_k) \Delta x$ $\int _a^b f(x) dx$ $f(x_2)$ $\Delta x$ $f(x_2) \Delta x$ $\lim _{n \to \infty } \sum _{k=0}^{n-1} f(x_k) \Delta x$