AP Calculus AB Unit 8 AP Classroom

What is the area of the region in the first quadrant bounded on the left by the graph of x=y^4+y^2 and on the right by the graph of x=5y?

A: 2.983

Over the time interval 0≤t≤10, a particle moves along the x-axis. The graph of the particle's velocity v(t) at time t is shown above. Over the time interval 0≤t≤10, the particle's displacement is 15 and the particle travels a total distance of 73. What is the total distance that the particle travels while moving to the left?

B: 29

Let R be the region in the first quadrant bounded by the graphs of x=y^2 and x=2y, as shown in the figure above. What is the area of R?

B: 4/3

A particle moves along the x-axis with velocity given by v(t)=4t−20sin(t^2+1) for time t≥0. If the particle is at position x=π at time t=0, which of the following gives the position of the particle at time t=4?

B: π+∫4, 0 (4t−20sin(t2+1))dt

The regions bounded by the graphs of y=6x and y=5x^2−x^3 are shaded in the figure above. The graphs intersect at x=0, x=2, and x=3. Which of the following gives the sum of the areas of the shaded regions?

B: ∫2, 0 (6x−(5x2−x3))ⅆx + ∫3, 2 ((5x2−x3)−6x)ⅆx

The graph of the continuous function f consists of three line segments, as shown above. What is the average value of f on the interval [−2,8]?

C: 2.3

The rate at which rain accumulates in a bucket is modeled by the function r given by r(t)=10t−t^2, where r(t) is measured in milliliters per minute and t is measured in minutes since the rain began falling. How many milliliters of rain accumulate in the bucket from time t=0 to time t=3?

C: 36

The regions bounded by the graphs of y=4x and y=x−x^2+x^3 are shaded in the figure above. What is the sum of the areas of the shaded regions?

C: 6.083

During a five-kilometer road race, runners pass a viewing stand. The rate at which runners pass the viewing stand over a certain 16-minute time interval is modeled by the continuous function R, where R(t) is measured in runners per minute and t is measured in minutes. The graph of R is shown in the figure above. How many runners pass the viewing stand between time t=0 and time t=16?

C: 610

The regions bounded by the graphs of y=2xπ and y=sinx are shaded in the figure above. Which of the following gives the sum of the areas of the shaded regions?

C: ∫0, -π/2 (2xπ−sinx)ⅆx + ∫π/2, 0 (sinx−2xπ)ⅆx

Let R be the region between the graph of y=lnx, the x-axis, and the line x=5. Which of the following gives the area of region R ?

C: ∫ln5, 0 (5−e^y)ⅆy

For time t≥0, the acceleration of an object moving in a straight line is given by a(t)=ln(3+t4). What is the net change in velocity from time t=1 to time t=5?

D: 16.868

If the average value of the function f on the interval 2≤x≤6 is 3, what is the value of ∫6, 2 (5f(x)+2)dx

D: 68

Let f be the function given by f(x)=3xsinx. What is the average value of f on the closed interval 1≤x≤7?

D: 8.161

The velocity of a particle moving along the x-axis is given by v(t)=e^(t−1)−1. Which of the following gives the total distance traveled by the particle over the time interval 0≤t≤3?

D: −∫1, 0 v(t) dt + ∫3, 1 v(t) dt