By hand, graph the following equations: Use your graphing calculator to evaluate the following integrals: What is the equation of:

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Presentation transcript:

By hand, graph the following equations: Use your graphing calculator to evaluate the following integrals: What is the equation of:

Step 1: Draw a Riemann rectangle of width dx in the region Step 2: Draw & LABEL line segments from the x-axis to both the Top & Bottom sides of the Riemann Rectangle Step 3: Find points of intersection (x=a and x=b) by setting y T = y B Step 4: Choose which formula to use depending on the WORDING :

Step 4W: Draw & LABEL line segments from the axis of revolución to Far & Near sides of the Riemann Rectangle Case I: Region R rotated about x-axis (y=0) axis of revolución Step 5W: Find equations for r o and r i in terms of y T, y B and k and sub into the x- washer formula.

Step 4W: Draw & LABEL segments from the axis of revolución to the X-Axis AND to the Far & Near sides of the Riemann Rectangle Case II: Region R rotated about the line y = -2 (AOR Below x-axis) axis of revolución Step 5W: Find equations for r o and r i in terms of y T, y B and # and sub into the x-washer formula.

Step 4W: Draw & LABEL segments from the axis of revolución to the X-Axis AND to the Far & Near sides of the Riemann Rectangle Case III: Region R rotated about the line y = +1 (AOR Between x-axis & R) axis of revolución Step 5W: Find equations for r o and r i in terms of y T, y B and # and sub into the x-washer formula.