(0.3470, 2.9404) -1 2 1 y y=2+ cos(x) y = csc(x) 2 (2.2962, 1.3365) 3 X Let R be the region bound by the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval 0≤x < x. a) Write, but do not solve, an equation involving integral expressions whose solution is the area of the region R. b) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis. c) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x = -1.
(0.3470, 2.9404) -1 2 1 y y=2+ cos(x) y = csc(x) 2 (2.2962, 1.3365) 3 X Let R be the region bound by the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval 0≤x < x. a) Write, but do not solve, an equation involving integral expressions whose solution is the area of the region R. b) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis. c) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x = -1.
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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Transcribed Image Text:(0.3470,
2.9404)
y = 2 + cos(x)
2-
(2.2962,
1.3365)
y = csc(x)
-1
2
Let R be the region bound by the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the
interval 0sx<7.
a) Write, but do not solve, an equation involving integral expressions whose solution is the area of
the region R.
b) Write, but do not solve, an equation involving integral expressions whose solution is the volume
of the solid generated when R is revolved around the x-axis.
c) Write, but do not solve, an equation involving integral expressions whose solution is the volume
of the solid generated when R is revolved around the line x = -1.
3.
1.
Transcribed Image Text:10
f6) = * + e*
(+ 1
2
2
5x2
+ 4x + 2
-2-
g(x) =
Let fand g be the functions defined by fx) = x+e-&* + 1, and g(x):
the two regions enclosed by the graphs of f and g shown in the figure above.
a) Find the sum of the areas of regions Q and R.
+ 4x + 2. Let Q and R be
2
3
b) The region Q is the base of a solid whose cross sections perpendicular to the x-axis are squares.
Find the volume of the solid.
c) The vertical line x = k divides region R into two equal regions with equal areas. Write, but do not
solve, an equation involving integral expressions whose solutions give the value k.
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