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Given: region R below bounded by the graphs of y = √x-3, y=9-x, and y = 0. (7,2) R (3,0) (9,0) (a) Find the area of R. (b) SET UP a (sum of) definite integral(s) that is equal to the arc length of the portion y = √x -3 which serves as a boundary of R. (c) Use the WASHER METHOD to set up (a sum of) definite integral(s) that is equal t generated when R is revolved about the line x = 9.

Given: region R below bounded by the graphs of y = √x-3, y=9-x, and y = 0. (7,2) R (3,0) (9,0) (a) Find the area of R. (b) SET UP a (sum of) definite integral(s) that is equal to the arc length of the portion y = √x -3 which serves as a boundary of R. (c) Use the WASHER METHOD to set up (a sum of) definite integral(s) that is equal t generated when R is revolved about the line x = 9.

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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Solve the following from a to d:

Given: region R below bounded by the graphs of y = √√x − 3, y = 9 — x, and y = 0. - (7,2) R (3,0) (9,0) (a) Find the area of R. (b) SET UP a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y = √√√x - 3 which serves as a boundary of R. (c) Use the WASHER METHOD to set up (a sum of) definite integral(s) that is equal to the volume generated when R is revolved about the line x = 9. (d) Set up a sum of definite integral(s) that is equal to the volume of the solid whose base is R and whose cross-sections perpendicular to the x-axis as equilateral triangles.
Transcribed Image Text:Given: region R below bounded by the graphs of y = √√x − 3, y = 9 — x, and y = 0. - (7,2) R (3,0) (9,0) (a) Find the area of R. (b) SET UP a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y = √√√x - 3 which serves as a boundary of R. (c) Use the WASHER METHOD to set up (a sum of) definite integral(s) that is equal to the volume generated when R is revolved about the line x = 9. (d) Set up a sum of definite integral(s) that is equal to the volume of the solid whose base is R and whose cross-sections perpendicular to the x-axis as equilateral triangles.
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