3- 2- y= g(x)- 1. R S 1 2 y = f(x) 5- 4+ 3+ 2 14 0 T 5) = (8(x))² HI 1 2 3 2. The function f is defined by f(x) = 3(1+x)05cos (2) for 0≤x≤ 3. The function g is continuous and decreasing for 0≤x≤ 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 arca 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))2 and the region T. 7' is the region bounded by the graph of y = (g(x))2 and the x- and y-axes. Region 7 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, cach 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.
3- 2- y= g(x)- 1. R S 1 2 y = f(x) 5- 4+ 3+ 2 14 0 T 5) = (8(x))² HI 1 2 3 2. The function f is defined by f(x) = 3(1+x)05cos (2) for 0≤x≤ 3. The function g is continuous and decreasing for 0≤x≤ 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 arca 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))2 and the region T. 7' is the region bounded by the graph of y = (g(x))2 and the x- and y-axes. Region 7 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, cach 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.
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
the function f is defined by f(x)=3(1 x)^0.5cos(pix/6)
i need the solution
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The figure above on the left shows the graphs of f and g and the regions R and S. R is the region bo:unded by
the graph of g and the x- and y-axcs. Region R has arca 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
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the graph of y = (g(x)) and thex- and y-axes. Region T has arca 5.32021.
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(a) Find the arca 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, cach cross section perpendicular to the x-axis is a roctangle
whosc height is 7 times the Iength of its basc in region S. Write, but do not evaluate, an integral expression
for the volume of this solid.
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