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The graphs of z = 8, y = h(z) (solid) and y = g(z) (dashed) are shown; the graph is not drawn to scale. Region One The points labeled are A- (8,4), B- (8,8), C (4,7), and D - (1,0). Suppose the portion of Region One in the First Quadrant is revolved around the z-axis. Select the expression(s) needed to find the volume of the solid of revolution formed when the region is revolved around the z-axis. * 9(2) dz ©**(g(=))² dz of "h(z) dz ©fx(h(z))³² dz f*(h(z))² dz **(9(2))² dx

The graphs of z = 8, y = h(z) (solid) and y = g(z) (dashed) are shown; the graph is not drawn to scale. Region One The points labeled are A- (8,4), B- (8,8), C (4,7), and D - (1,0). Suppose the portion of Region One in the First Quadrant is revolved around the z-axis. Select the expression(s) needed to find the volume of the solid of revolution formed when the region is revolved around the z-axis. * 9(2) dz ©**(g(=))² dz of "h(z) dz ©fx(h(z))³² dz f*(h(z))² dz **(9(2))² dx

Advanced Engineering Mathematics
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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The graphs of -8, y = h(z) (solid) and y = g(z) (dashed) are shown; the graph is not drawn to scale. Region One The points labeled are 4 = (8,4), B = (8,8), C = (4,7), and D = (1, 0). Suppose the portion of Region One in the First Quadrant is revolved around the z-axis. Select the expression(s) needed to find the volume of the solid of revolution formed when the region is revolved around the z-axis. g(x) ©f*9(2) dz of**(g(z))² dz ofh(z) d © f*x(h(2))² dx *7(h(z))² dz f₁** (9(2))²³ dz
Transcribed Image Text:The graphs of -8, y = h(z) (solid) and y = g(z) (dashed) are shown; the graph is not drawn to scale. Region One The points labeled are 4 = (8,4), B = (8,8), C = (4,7), and D = (1, 0). Suppose the portion of Region One in the First Quadrant is revolved around the z-axis. Select the expression(s) needed to find the volume of the solid of revolution formed when the region is revolved around the z-axis. g(x) ©f*9(2) dz of**(g(z))² dz ofh(z) d © f*x(h(2))² dx *7(h(z))² dz f₁** (9(2))²³ dz
Expert Solution
Step 1

Given functions are 

x = 8 , y = h(x)(solid line) , y = g(x) ( dashed line ).

and the points are 

A(8,4) , B(8,8) , C(4,7) , D(1,0).

we have to find out the integral for the region when revolved around the x axis.

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