Calculus AB Unit 8 Review

 $What\ is\ the\ average\ value\ of\ F\left(x\right)=x^2-x-2\ over\ the\ interval\ \left[-1,4\right]?$  

•  $\frac{-2}{3}$  

•  $\frac{5}{6}$  

•  $\frac{-10}{3}$  

•  $\frac{25}{6}$  

Patrick is drinking water throughout the day and the rate at which he drinks water is given by the differentiable function W, where W(t) is measured in cups per day and t is measured in days. Which of the following expressions gives Patrick's average amount of water, in cups per day, he drank from t=0 to t=4 days?

• $\frac{1}{4}\int_0^4W\left(t\right)dt$

• $\frac{1}{4}\int_0^4W'\left(t\right)dt$

• $\int_0^4W\left(t\right)dt$

• $\int_0^4W'\left(t\right)dt$

 $v\left(t\right)=\cos\left(t\right)\ \ \ for\ \ \ t\ge0$  

A particle moves along a straight line. The velocity of the particle is given by the differentiable function above. What is the total distance traveled by the particle from t=0 to t=2pi?

• 0

• 2

• 4

• 6

 $\ y=\frac{1}{x+2},\ y=\left(x+2\right)^2,\ x=\frac{-3}{2},\ and\ x=1.$  Determine the area of the region bounded by the above equations.

• -7.1665

• 7.970

• -0.4014

• 7.1665

The shaded region above is revolved around the line y=1 to create a solid. Using the "disc method" which integral gives the volume of the solid?

• $\int_0^1\pi\left(e^x-1\right)dx$

• $\int_0^e\pi\left(e^x-1\right)dx$

• $\int_0^1\pi\left(e^{2x}-1\right)dx$

• $\int_0^1\pi\left(e^x-1\right)^2dx$

 A region R, enclosed by the function  $y=\sqrt{x-1}$   , the x-axis and the vertical line x=5, is revolved about the y-axis. Which of the following integral expressions give the volume of this solid?

•  $\pi\int_0^2\left(25-\left(y^2+1\right)^2\right)dy$  

•  $\pi\int_0^5\left(25-\left(y^2+1\right)^2\right)dy$  

•  $\pi\int_0^2\left(\left(y^2+1\right)^2-25\right)dy$  

•  $\pi\int_0^5\left(\left(y^2+1\right)^2-25\right)dy$  

• $\int_0^6\pi\left(6x-x^{2\ }\right)^2dx\ \$

• $\int_0^62\pi x\left(6x-x^{2\ }\right)^{ }dx$

• $\int_0^6\pi x\left(6x-x^{2\ }\right)^2dx$

• $\int_0^6\pi\left(6x-x^2\right)^{ }dx$

Let R'(t) be a differentiable function and represent the rate at which tea, measured in gallons per hour, is poured into a beverage machine. At t=0, there are 10 gallons of tea in the machine. Which expression gives the total amount of tea in the machine at t=6 hours?

•  $\int_0^6R\left(t\right)dt$  

•  $10+\int_0^6R\left(t\right)dt$  

•  $\int_0^6R'\left(t\right)dt$  

•  $10+\int_0^6R'\left(t\right)dt$  

Find the area between the curves:

 $x=y^2-3$  
 $x=2y-3$  

• 1.333

• 2.333

• 1.666

• 2.111

 $y=e^{x\ }and\ the\ lines\ y=1\ and\ x=\ln3$  

The base of a solid is the region enclosed by the above functions. Cross-sections perpendicular to the y-axis are squares. Write an integral that represents the volume of the solid.

•  $\pi\int_1^3\left(\ln3-\ln y\right)^2dy$  

•  $\int_1^3\left(\ln3-\ln y\right)^2dy$  

•  $\int_0^{\ln3}\left(\ln3-\ln y\right)^2dy$  

•  $\int_1^3\left(\left(\ln3\right)^2-\left(\ln y\right)^2\right)^{ }dy$