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. (1,3) (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. 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)
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. (1,3) (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. 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)
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.
%3D
(0, 4)
(a) Set up a (sum of) definite integral(s) with
respect to x that is equal to the area of R.
(1,3)
(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.
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb2cd596-c79f-49d7-ba41-f1e477389469%2F46385001-2ac2-4ad5-af0c-6d3cd67386b2%2F9h01rer_processed.jpeg&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.
%3D
(0, 4)
(a) Set up a (sum of) definite integral(s) with
respect to x that is equal to the area of R.
(1,3)
(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.
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)
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