Calculus: Volumes of Revolution

Which method is introduced as potentially easier than the washer and disk method?

• Method of spherical shells

• Method of cylindrical shells

• Method of conical shells

• Method of cubic shells

What is the basic formula for calculating volumes using the cylindrical shells method when rotating about the y-axis?

• 2π ∫ from A to B (x)(f(x) - g(x)) dx

• π ∫ from A to B (f(x)^2 - g(x)^2) dx

• π ∫ from A to B (x^2) dx

• 2π ∫ from A to B (f(x) + g(x)) dx

What function is used in the specific example discussed?

• y = cos(x^2)

• y = x^2

• y = sin(x^2)

• y = tan(x^2)

What is the shell radius when rotating about the line x = -4?

• X + 4

• X

• X - 4

• 4 - X

What is the new shell radius when rotating about the line x = 10?

• 10 - X

• X + 10

• X

• 10 + X

What changes when rotating the same region about a different line?

• Method of integration

• Limits of integration

• Shell height

• Shell radius

When rotating about a horizontal line, what becomes the focus in the formula?

• 2π in the formula

• π in the formula

• X's in the formula

• Y's in the formula

What is the shell radius when rotating about the line y = -3?

• Y - 3

• 3 - Y

• Y

• Y + 3

What is the shell height for the region rotated about the line y = -3?

• Y + Y^2

• Y^2 - Y

• Y - Y^2

• 2Y

Which method can be used interchangeably with the cylindrical shells method, depending on the situation?

• Cubic shells method

• Conical shells method

• Spherical shells method

• Washer and disk method