3. Let R be the region below bounded by the parabola y = 4 - 2² and the lines 3x - 2y +3=0 and y = 0. (0,4) (a) Set up a (sum of) definite integral(s) with respect to a that is equal to the area of R. (b) Set up a definite integral that is equal to the arc length of the portion of the parabola y = 4 - x² 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 of the solid generated when R is revolved about the line x = 2. (-2,0) R (-1,0) (1,3) 2
3. Let R be the region below bounded by the parabola y = 4 - 2² and the lines 3x - 2y +3=0 and y = 0. (0,4) (a) Set up a (sum of) definite integral(s) with respect to a that is equal to the area of R. (b) Set up a definite integral that is equal to the arc length of the portion of the parabola y = 4 - x² 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 of the solid generated when R is revolved about the line x = 2. (-2,0) R (-1,0) (1,3) 2
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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![3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y +3=0
and y = 0.
(0,4)
(a) Set up a (sum of) definite integral(s) with
respect to x that is equal to the area of R.
R
(b) Set up a definite integral that is equal to the arc
length of the portion of the parabola y = 4 - x²
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 of
the solid generated when R is revolved about the
line x = 2.
(-2,0)
(-1,0)
(1,3)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa876f0ef-bb5d-4c75-a8d5-4baaa8ac3f10%2F92725eb4-b8e5-4207-8ff7-16417d7525fd%2F0dtwpzo_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y +3=0
and y = 0.
(0,4)
(a) Set up a (sum of) definite integral(s) with
respect to x that is equal to the area of R.
R
(b) Set up a definite integral that is equal to the arc
length of the portion of the parabola y = 4 - x²
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 of
the solid generated when R is revolved about the
line x = 2.
(-2,0)
(-1,0)
(1,3)
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