T3 - 12A- AL FAROUQ 2022

Find the area of the region bounded by the graphs of y = x² and y = 4x.

• 32/3

• 64/3

• 32

• 64

• 32/5

 $A_1+A_2=$  

• 
• 
• 
• 

• A

• B

• C

• D

Use the shell method to set up and evaluate the volume created by rotating the following curve about the y-axis.
 $y=3\sqrt{x}$  

•  $\frac{192\pi}{5}$  

•  $\frac{384\pi}{7}$  

•  $\frac{192\pi}{7}$  

•  $\frac{384\pi}{5}$  

•  $\frac{96\pi}{5}$  

What is the volume of the solid formed in the second quadrant bounded by the curves         y = 9 – x², the x-axis and the y-axis when it is rotated about the line x = 1?

• 153π/2
• 81π/2
• 648π/5
• 45π/2

For each problem, find the volume of the solid that results when the region enclosed by the curves is revolved about the y-axis. Set up, but do not evaluate the integral.

• A

• B

• C

• D

• A

• B

• C

• D

• disk
• washer
• shell

• A

• B

• C

• D

Describe the cross section.

• triangle
• rectangle
• trapezoid
• square