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X Z=1 R N -x=ln4 x = ln (t + 2), (e) Find the area of R. Consider a structure D with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2. D occupies the region below the surface z = f(x,y) = 1 +Y and above the region R on the xy-plane. R is bounded by the planes y=0, x=In2, x=In4 and the curve C which is parametrised by y = (t+1) Curve C x=ln2 Area of R t> -1 (c) 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 (d) Show that the area can be expressed in terms of the following single integral Sa+D){ t + 27 de

X Z=1 R N -x=ln4 x = ln (t + 2), (e) Find the area of R. Consider a structure D with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2. D occupies the region below the surface z = f(x,y) = 1 +Y and above the region R on the xy-plane. R is bounded by the planes y=0, x=In2, x=In4 and the curve C which is parametrised by y = (t+1) Curve C x=ln2 Area of R t> -1 (c) 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 (d) Show that the area can be expressed in terms of the following single integral Sa+D){ t + 27 de

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 44AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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1. Change of Variable of Integration in 2D [ 1(x, y) dxdy = f(x(u, v),y(u, v))|J(u, v)| dudv 2. Transformation to Polar Coordinates 3. Change of Variable of Integration in 3D JJJ. [ f(x,y, 2) dxdydz = [[[_ F(u,v, w)|J(u, v, w)| dudvdw x=r cos 0, y =rsin 0, J(,0)=r 4. Transformation to Cylindrical Coordinates 5. Transformation to Spherical Coordinates 6. Line Integrals x = r cos 0, y = r sin 0, z = 2, J(r,0,2)=r x = r cos@sind, y=rsin sind, z=rcos, J(r,0,0) = r² sin 7. Work Integrals [ f(x, y, z) ds = [* f(x(1), y(t), =(0)) √/x'(0}² +y°(1)² +2{t}°dt dx dz dt [F(x, y, z) - dr = -C = [° F + F + F = d 8. Surface Integrals [[ 91,9, 2) ds = [[ 9(2.v. f(x,y) √/ S3 + f2 + 1 dxdy R 9. Flux Integrals For a surface with upward unit normal, = 11₁₂₁-B₁ II.F. FindS -Fifz-F₂fy + F3 dydx
Transcribed Image Text:1. Change of Variable of Integration in 2D [ 1(x, y) dxdy = f(x(u, v),y(u, v))|J(u, v)| dudv 2. Transformation to Polar Coordinates 3. Change of Variable of Integration in 3D JJJ. [ f(x,y, 2) dxdydz = [[[_ F(u,v, w)|J(u, v, w)| dudvdw x=r cos 0, y =rsin 0, J(,0)=r 4. Transformation to Cylindrical Coordinates 5. Transformation to Spherical Coordinates 6. Line Integrals x = r cos 0, y = r sin 0, z = 2, J(r,0,2)=r x = r cos@sind, y=rsin sind, z=rcos, J(r,0,0) = r² sin 7. Work Integrals [ f(x, y, z) ds = [* f(x(1), y(t), =(0)) √/x'(0}² +y°(1)² +2{t}°dt dx dz dt [F(x, y, z) - dr = -C = [° F + F + F = d 8. Surface Integrals [[ 91,9, 2) ds = [[ 9(2.v. f(x,y) √/ S3 + f2 + 1 dxdy R 9. Flux Integrals For a surface with upward unit normal, = 11₁₂₁-B₁ II.F. FindS -Fifz-F₂fy + F3 dydx
X Z=1 R ii. N -x=ln4 x = ln(t + 2), (e) Find the area of R. Y Consider a structure D with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2. D occupies the region below the surface z = f(x, y) = 1 and above the region R on the xy-plane. R is bounded by the planes y=0, x=In2, x-In4 and the curve C which is parametrised by Curve C x=ln2 y = (t+1) t> -1 (c) Express the area of R (and thus the volume of D) in terms of integral(s) using: i. Horizontal strip method Vertical strip method (d) Show that the area can be expressed in terms of the following single integral Area of R = (t + 1)(t + 2)ª dt
Transcribed Image Text:X Z=1 R ii. N -x=ln4 x = ln(t + 2), (e) Find the area of R. Y Consider a structure D with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2. D occupies the region below the surface z = f(x, y) = 1 and above the region R on the xy-plane. R is bounded by the planes y=0, x=In2, x-In4 and the curve C which is parametrised by Curve C x=ln2 y = (t+1) t> -1 (c) Express the area of R (and thus the volume of D) in terms of integral(s) using: i. Horizontal strip method Vertical strip method (d) Show that the area can be expressed in terms of the following single integral Area of R = (t + 1)(t + 2)ª dt
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