Volume Calculation Using the Washer Method

The video tutorial explains how to calculate the volume of a region bounded by two functions when rotated about the x-axis and y-axis using the washer method. It covers the setup of integrals, determination of outer and inner radii, and the calculation of volumes for both axes of rotation. The tutorial emphasizes the importance of understanding the geometry of the region and the application of calculus techniques to solve the problem.

What are the functions that define the boundaries of region R?

• F(x) = x^2 and G(x) = x/4

• F(x) = x^2 and G(x) = sqrt(x)

• F(x) = sqrt(x) and G(x) = x/4

• F(x) = x/4 and G(x) = sqrt(x)

What method is used to find the volume of the solid when rotating about the x-axis?

• Cavalieri's Principle

• Shell Method

• Disk Method

• Washer Method

What is the outer radius function R(x) when rotating about the x-axis?

• R(x) = x/4

• R(x) = sqrt(x)

• R(x) = x^2

• R(x) = 4x

What is the thickness of the representative rectangle when rotating about the x-axis?

• Delta y

• Delta x

• Delta z

• Delta t

What is the result of the integral for the volume when rotating about the x-axis?

• 256 pi cubic units

• 128/3 pi cubic units

• 256/3 pi cubic units

• 128 pi cubic units

What is the point of intersection of the two functions?

• (4, 0) and (0, 16)

• (0, 4) and (16, 0)

• (0, 0) and (4, 16)

• (0, 0) and (16, 4)

When rotating about the y-axis, what is the outer radius function R(y)?

• R(y) = y^2

• R(y) = 4y

• R(y) = sqrt(y)

• R(y) = y/4

What is the inner radius function r(y) when rotating about the y-axis?

• r(y) = y/4

• r(y) = y^2

• r(y) = 4y

• r(y) = sqrt(y)

What is the result of the integral for the volume when rotating about the y-axis?

• 1024/15 pi cubic units

• 2048/15 pi cubic units

• 2048/3 pi cubic units

• 1024/3 pi cubic units

What is the thickness of the representative rectangle when rotating about the y-axis?

• Delta z

• Delta y

• Delta x

• Delta t