Let R be the region bounded by the x-axis and the graphs of and y = 4 – 2.x , as shown in the figure above. 1+ x? (a) Find the area of R.

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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Let R be the region bounded by the x-axis and the graphs of
y =
1+ x²
and y = 4 – 2x , as shown in the figure above.
y = 4 – 2x
(a) Find the area of R.
y =
1+ x?
b) Find the volume of the solid generated when R is revolved around the line y = -2.
(c) The region R is the base of a solid. For this solid, each cross section perpendicular
to the x-axis is a semicircle. Find the volume of the solid.
Transcribed Image Text:2. (Calculator Active) Let R be the region bounded by the x-axis and the graphs of y = 1+ x² and y = 4 – 2x , as shown in the figure above. y = 4 – 2x (a) Find the area of R. y = 1+ x? b) Find the volume of the solid generated when R is revolved around the line y = -2. (c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a semicircle. Find the volume of the solid.
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