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Please answer this question to the best of your ability. You are welcome to re-watch parts of any of the videos to help you.

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


t in seconds	1	4	7	10	13

v(t) in m/s	2	5	7	8	9

Which of the following is an approximation to $\int _4^{10} v(t) dt$ ?

$93$ meters $60$ meters $36$ meters $31$ meters $12$ meters None of the above

Use the graph of the rate, $y=R(t)$ , to answer the following question:

Which value is greatest?

$\int _1^{10} R(t) dt$ $\int _2^{11} R(t) dt$ $\sum _{k=0}^{2} R(2 + k \times \Delta t) \Delta t$ where $\Delta t = 3$ $\sum _{k=0}^{2} R(2 + k \times \Delta t) \Delta t$ where $\Delta t = 1$ None of the above More information is needed

The following picture illustrates a Riemann sum:

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

$\Delta x$ $f(x_2)$ $f(x_2) \Delta x$ $\sum _{k=0}^7 f(x_k) \Delta x$ $\int _a^b f(x) dx$ $\lim _{n \to \infty } \sum _{k=0}^{n-1} f(x_k) \Delta x$