There is a shape at the centre of the structure from the floor to the roof. Below is the position of the x and y coordinates. (a) (b) (c) (d) Position 1 2 3 4 5 5 to 1 (f) x coordinate y coordinate B 0 B A - B A - B 0 0 - B A quarter-circle: x² + y² = B² Present the shape by joining all points in FOUR straight lines and ONE quarter-circle. Write down the equation for the FOUR straight lines and ONE quarter-circle. Double Integral Determine the value of the upper and lower limits of x1, x2, yl, and y2. Find the volume of the pillar and explain the working steps. ry2 y1 x2 m² Change Order of Double Integral Determine the value of the upper and lower limits of x3, x4, y3, and y4. Find the volume of the pillar and explain the working steps. cx4 y4 * *z(x, y) dy dx x3 y3 MATLAB or OCTAVE Method (e) Find the pillar volume by using MATLAB or OCTAVE (integral2 function). Use those limits stated in part 2(c). y2 z(x,y) dx dy y1 x2 * x1 z(x,y) dx dy Comments on the results for part 2(c), 2(d), and 2(e).
There is a shape at the centre of the structure from the floor to the roof. Below is the position of the x and y coordinates. (a) (b) (c) (d) Position 1 2 3 4 5 5 to 1 (f) x coordinate y coordinate B 0 B A - B A - B 0 0 - B A quarter-circle: x² + y² = B² Present the shape by joining all points in FOUR straight lines and ONE quarter-circle. Write down the equation for the FOUR straight lines and ONE quarter-circle. Double Integral Determine the value of the upper and lower limits of x1, x2, yl, and y2. Find the volume of the pillar and explain the working steps. ry2 y1 x2 m² Change Order of Double Integral Determine the value of the upper and lower limits of x3, x4, y3, and y4. Find the volume of the pillar and explain the working steps. cx4 y4 * *z(x, y) dy dx x3 y3 MATLAB or OCTAVE Method (e) Find the pillar volume by using MATLAB or OCTAVE (integral2 function). Use those limits stated in part 2(c). y2 z(x,y) dx dy y1 x2 * x1 z(x,y) dx dy Comments on the results for part 2(c), 2(d), and 2(e).
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
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A=4,B=2
Transcribed Image Text:2.
There is a shape at the centre of the structure from the floor to the roof.
Below is the position of the x and y coordinates.
(a)
(b)
(c)
(d)
Position
1
2
3
4
5
5 to 1
(f)
y coordinate
0
A
A
0
- B
A quarter-circle: x² + y² = B²
x coordinate
B
B
- B
- B
0
Present the shape by joining all points in FOUR straight lines
and ONE quarter-circle.
Write down the equation for the FOUR straight lines and ONE
quarter-circle.
Double Integral
Determine the value of the upper and lower limits of x1, x2, y1,
and y2. Find the volume of the pillar and explain the working
steps.
ry2
17²2 17²3²0
y1
So
z(x, y) dx dy
Change Order of Double Integral
Determine the value of the upper and lower limits of x3, x4, y3,
and y4. Find the volume of the pillar and explain the working
steps.
x4
ry4
[x* [* z(x, y) dy dx
x3
y3
MATLAB or OCTAVE Method
(e) Find the pillar volume by using MATLAB or OCTAVE
(integral2 function). Use those limits stated in part 2(c).
y2
x2
[X² [²²₂x,
z(x, y) dx dy
y1 x1
Comments on the results for part 2(c), 2(d), and 2(e).
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