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Let R be the region in the first quadrant bounded by the graphs of y = √√8-x², y = x, and the x-axis. Let S be the solid formed by revolving the region R about the x-axis. Complete the items below. Include enough detail that a Calculus I student would be able to follow each step of your work. Please use correct mathematical notation and label graphs appropriately. 2. 1. Sketch the two dimensional region R. Label each boundary of the region with a corresponding equation. Set up an integral with respect to x representing the volume of the solid S. Identify which method you used (disk/washer or shell) and evaluate this integral. 3. Set up an integral with respect to y representing the volume of the solid S. Identify which method you used (disk/washer or shell) and evaluate this integral.

Let R be the region in the first quadrant bounded by the graphs of y = √√8-x², y = x, and the x-axis. Let S be the solid formed by revolving the region R about the x-axis. Complete the items below. Include enough detail that a Calculus I student would be able to follow each step of your work. Please use correct mathematical notation and label graphs appropriately. 2. 1. Sketch the two dimensional region R. Label each boundary of the region with a corresponding equation. Set up an integral with respect to x representing the volume of the solid S. Identify which method you used (disk/washer or shell) and evaluate this integral. 3. Set up an integral with respect to y representing the volume of the solid S. Identify which method you used (disk/washer or shell) and evaluate this integral.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let R be the region in the first quadrant bounded by the graphs of y = √√8-x², y = x, and the x-axis. Let S be the solid formed by revolving the region R about the x-axis. Complete the items below. Include enough detail that a Calculus I student would be able to follow each step of your work. Please use correct mathematical notation and label graphs appropriately. 2. 1. Sketch the two dimensional region R. Label each boundary of the region with a corresponding equation. Set up an integral with respect to x representing the volume of the solid S. Identify which method you which used (disk/washer or shell) and evaluate this integral. 3. Set up an integral with respect to y representing the volume of the solid S. Identify which method you used (disk/washer or shell) and evaluate this integral. 4. Compare and discuss the two integrals, addressing each of the questions below. In your writing, imagine that your audience is your Calculus II classmates. a. Which method would you recommend to a fellow student? Why? b. What errors might a student make when using an integral in terms of x? c. What errors might a student make when using an integral in terms of y? d. Present and work an example of a problem that would be better solved using the other method. (The one that you did not recommend in part a.)
Transcribed Image Text:Let R be the region in the first quadrant bounded by the graphs of y = √√8-x², y = x, and the x-axis. Let S be the solid formed by revolving the region R about the x-axis. Complete the items below. Include enough detail that a Calculus I student would be able to follow each step of your work. Please use correct mathematical notation and label graphs appropriately. 2. 1. Sketch the two dimensional region R. Label each boundary of the region with a corresponding equation. Set up an integral with respect to x representing the volume of the solid S. Identify which method you which used (disk/washer or shell) and evaluate this integral. 3. Set up an integral with respect to y representing the volume of the solid S. Identify which method you used (disk/washer or shell) and evaluate this integral. 4. Compare and discuss the two integrals, addressing each of the questions below. In your writing, imagine that your audience is your Calculus II classmates. a. Which method would you recommend to a fellow student? Why? b. What errors might a student make when using an integral in terms of x? c. What errors might a student make when using an integral in terms of y? d. Present and work an example of a problem that would be better solved using the other method. (The one that you did not recommend in part a.)
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