6 3 4- 3- y = g(x)- T R 2. The function f is defined by f(x) = 3(1 + x)0-Scos( for 0 Sx S 3. The function g is continuous and decreasing for 0 SxS 3 with g(3) = 0. The figure above on the left shows the graphs of f and g and the regions R and S. R is the region bounded b the graph of g and the x- and y-axes. Region R has area 3.24125. S is the region bounded by the y-axis and the graphs of f and g. The figure above on the right shows the graph of y = (g(x)) and the region T. T is the region bounded by the graph of y = (g(x))² and the x- and y-axes. Region T has area 5.32021. (a) Find the area of region S. (b) Find the volume of the solid generated when region S is revolved about the horizontal line y = -3. (c) Region S is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a rectangle whose height is 7 times the length of its base in region S. Write, but do not evaluate, an integral expressi for the volume of this solid. %24 2. 2.

6 3 4- 3- y = g(x)- T R 2. The function f is defined by f(x) = 3(1 + x)0-Scos( for 0 Sx S 3. The function g is continuous and decreasing for 0 SxS 3 with g(3) = 0. The figure above on the left shows the graphs of f and g and the regions R and S. R is the region bounded b the graph of g and the x- and y-axes. Region R has area 3.24125. S is the region bounded by the y-axis and the graphs of f and g. The figure above on the right shows the graph of y = (g(x)) and the region T. T is the region bounded by the graph of y = (g(x))² and the x- and y-axes. Region T has area 5.32021. (a) Find the area of region S. (b) Find the volume of the solid generated when region S is revolved about the horizontal line y = -3. (c) Region S is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a rectangle whose height is 7 times the length of its base in region S. Write, but do not evaluate, an integral expressi for the volume of this solid. %24 2. 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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Question

4
6.
4
v= (g(x))?
2
3
y = g(x)-
2
T
EX
0.5
2. The function f is defined by f(x) = 3(1 + x)0 cos
for 0 Sx S 3. The function g is continuous and
decreasing for 0 SxS 3 with g(3) = 0.
The figure above on the left shows the graphs of f and g and the regions R and S. R is the region bounded by
the graph of g and the x- and y-axes. Region R has area 3.24125. S is the region bounded by the y-axis and
the graphs of f and g.
The figure above on the right shows the graph of y = (g(x)) and the region T. T is the region bounded by
the graph of y = (g(x))² and the x- and y-axes. Region T has area 5.32021.
(a) Find the area of region S.
(b) Find the volume of the solid generated when region S is revolved about the horizontal line y = -3.
(c) Region S is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a rectangle
whose height is 7 times the length of its base in region S. Write, but do not evaluate, an integral expression
for the volume of this solid.

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