Setting up integrals using the washer method:

• The washer method involves calculating the volume of a solid of revolution as the sum of the volumes of a series of washers
• The axis of revolution dictates the variable of integration in the washer method


  True
• When the axis of revolution is horizontal, we integrate with respect to x
• The outer radius $R(x)$ represents the distance from the axis of revolution to the outer
• Steps to use the washer method to find the volume of a solid of revolution

  1️⃣ Identify the curve that generates the solid

  2️⃣ Determine the limits of integration

  3️⃣ Set up the integral using the washer method formula
• Match the axis of revolution with the corresponding variable of integration:

  Horizontal axis ↔️ x

  Vertical axis ↔️ y
• The key steps to set up the integral using the washer method begin with identifying the generating curve
• Match the axis of revolution with the correct variable of integration:

  Horizontal ↔️ x

  Vertical ↔️ y
• When rotating the region bounded by $y =$$x^{2}$ and $y =$$4$ around the x-axis, the outer radius is $R(x) =$$4$ and the inner radius is $r(x) =$$x^{2}$, resulting in integration with respect to x
• Steps to determine the outer radius $R(x)$


  1️⃣ Identify the outer boundary function

  2️⃣ Express the function in terms of x or y

  3️⃣ Set $R(x)$ equal to the absolute value of the function
• The function $f(x)$ in the washer method formula represents the outer radius.


  True
• When using the washer method, the limits of integration define the boundaries within which the solid is formed
• The intersection points of $y =$$x^{2}$ and $y =$$4$ are at $x =$$\pm 2$.


  True
• Steps to set up the integral using the washer method

  1️⃣ Identify the curve that generates the solid

  2️⃣ Determine the limits of integration

  3️⃣ Set up the integral using the washer method formula
• Match the axis of revolution with the corresponding variable of integration:

  Horizontal axis ↔️ x

  Vertical axis ↔️ y
• If the axis of revolution is vertical, the radii functions are expressed in terms of y


  True
• If the region bounded by y = x^{2}</latex> and $y =$$4$ is rotated around the x-axis, the outer radius is $R(x) =$$4$


  True
• When using the washer method, the axis of revolution dictates the variable of integration
• What is the volume of a solid of revolution calculated as in the washer method?

  Sum of washer volumes
• The washer method formula is V = \pi \int_{a}^{b} [f(x)]^{2} - [g(x)]^{2} dx</latex>

  True
• What is the variable of integration when rotating around the y-axis?

  y
• The outer radius $R(x)$ is the distance from the axis of revolution to the outer curve.


  True
• What does the inner radius r(x)</latex> represent in the washer method?

  Distance to inner curve
• What does the function $g(x)$ represent in the washer method formula?


  Inner radius
• Steps to find the limits of integration

  1️⃣ Sketch the region

  2️⃣ Find intersection points

  3️⃣ Determine the integration range