Calculus 6.1-6.2 Review

This is the region you should have selected. If you wanted to find the area of the region, what kind of rectangle should you draw and therefore which variable should you integrate with respect to? (Select 2 answers.)

• Horizontal Rectangle

• Vertical Rectangle

• Integrate with respect to x

  (dx problem)

• Integrate with respect to y

  (dy problem)

When calculating volumes of revolution using the disk or washer method, the rectangle should always be drawn ________ to your axis of rotation.

• parallel

• perpendicular

• it doesn't matter

How do you determine if you have a disk or washer problem when calculating volumes of revolution?

• If you have a dx problem, its always a disk problem and if you have a dy problem, its always a washer problem.

• If there's no space between your region and axis of rotation, it's a washer problem. If there's space between your region and axis of rotation, it's a disk problem.

• If there's no space between your region and axis of rotation, it's a disk problem. If there's space between your region and axis of rotation, it's a washer problem.

• It doesn't matter, you can do whichever you want.

We now want to know the volume of the region rotated about the x-axis. What kind of rectangle should you draw and therefore which variable should you integrate with respect to? (Select 2 answers.)

• Horizontal Rectangle

• Vertical Rectangle

• Integrate with respect to x

  (dx problem)

• Integrate with respect to y

  (dy problem)

We now want to know the volume of the region rotated about the x-axis. Is this a disk or a washer problem?

• Disk Problem

• Washer Problem

We now want to know the volume of the region rotated about the y-axis. What kind of rectangle should you draw and therefore which variable should you integrate with respect to? (Select 2 answers.)

• Horizontal Rectangle

• Vertical Rectangle

• Integrate with respect to x

  (dx problem)

• Integrate with respect to y

  (dy problem)

We now want to know the volume of the region rotated about the y-axis. Is this a disk problem or a washer problem?

• Disk Problem

• Washer Problem

This is the region you should have selected. What kind of rectangle should you draw and therefore which variable should you integrate with respect to? (Select 2 answers.)

• Horizontal Rectangle

• Vertical Rectangle

• Integrate with respect to x

  (dx problem)

• Integrate with respect to y

  (dy problem)