Z=1 Z x=ln4 STRUCTURE D 3 Y = (++) " Curve C x=In2 Consider a structure D with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2.0 occupies the region below the surface z = f(x,y) =1 and above the region on the xy-plane. R is bounded by the planes y=0, x-in2, x-In4 and the curve C which is parametrised by x= In (t+2) 7x41 i. Write down an expression for the arc length of C between its intersection points with x-In4 and In2 (blue dots in Structure D). Leave the expression in integral form. ii. Express the equation for the curve C in y=f(x) form. Express the area of R (and thus the volume of D) in terms of integral(s) using: i Horizontal strip method ii. Vertical strip method iv. Show that the area can be expressed in terms of the following single integral of B = S₂ (E+¹1)(4+2) at
Z=1 Z x=ln4 STRUCTURE D 3 Y = (++) " Curve C x=In2 Consider a structure D with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2.0 occupies the region below the surface z = f(x,y) =1 and above the region on the xy-plane. R is bounded by the planes y=0, x-in2, x-In4 and the curve C which is parametrised by x= In (t+2) 7x41 i. Write down an expression for the arc length of C between its intersection points with x-In4 and In2 (blue dots in Structure D). Leave the expression in integral form. ii. Express the equation for the curve C in y=f(x) form. Express the area of R (and thus the volume of D) in terms of integral(s) using: i Horizontal strip method ii. Vertical strip method iv. Show that the area can be expressed in terms of the following single integral of B = S₂ (E+¹1)(4+2) at
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:Z=1
N
-x=In4
Ex
STRUCTURE D
"
Curve C
x=In2
Consider a structure with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2.0 occupies the region
below the surface
z = f(xx,y) =1
and above the region on the xy-plane.
Ris bounded by the planes y=0, x=ln2, x-ln4 and the curve C which is parametrised by
x= In (t+2)
> y = (++)
774
i. Write down an expression for the arc length of C between its intersection points with x-In4 and Im2 (blue dots in Structure
D). Leave the expression in integral form.
ii. Express the equation for the curve C in y=f(x) form.
Express the area of R (and thus the volume of D) in terms of integral(s) using:
i. Horizontal strip method
ii. Vertical strip method
iv. Show that the area can be expressed in terms of the following single integral
Area of B = So (E+1)(4+2)
at
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