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