For time t ≥ 0, the velocity of a particle moving along the x-axis is given by

For time t ≥ 0, the velocity of a particle moving along the x-axis is given by v(t) = x3 - 3x2 + x. The initial position of the particle at time t = 0 is x = 3. Which of the following gives the total distance the particle traveled from time t = 0 to time t = 4?

Question 2

What is the average value of

on the closed interval [1, 3]?

Question 3

Which definite integral represents the area of the region that is bounded by 3x + 3y2 = 0 and y = 2x + 1?

Question 4

A certain mosquito population changes at the rate M(t) = 12.1(1.2)t mosquitos per day, where t represents time in days.

If the mosquito population is 649 at t = 0, then how many mosquitos are there on day 5? Round to the nearest whole number.

99

735

748

Question 5

The water level of a certain body of water is changing at a rate of

inches per hour, where t represents hours since 12 a.m.

Part A: Using correct units, explain the meaning of

in terms of the context of this problem. (1 point)

Part B: Write the integral that represents the number of inches that the water level changes from 10 a.m. to 3 p.m.

Part C: Use your calculator to evaluate your integral from Part B. Explain the meaning of the answer in terms of the context.

Part D:What is the average hourly number of inches that the water level changes for this lake in one day?

Question 6

For the regions A and B shown in the graph: Part A: Discuss the limits of integration.

Part B: Set up an integral expression that represents the total area. Part C: Calculate the total area.