Video Set Introduction

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Before watching the videos, think about and answer these questions to the best of your ability.

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 28 30 42 44 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 definition of the definite integral represents the green shaded region?

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