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 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) 3

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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)
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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