Problem #6: Let S be the portion of the plane 3x + 4y +z = 7 within the solid cylindrical region x² + y2 ≤ 1.(a) Compute the surface area of S.(b) Let S be oriented so the unit normal on S has a positive z-component and let F be the vector fieldF(x, y, z)4x²i+ 3y²j+=k.Compute the flux of F through S, i.e. the surface integralSSS(A)√13 π (B) √√26 π (C) √√2 π (D) 10 (E)FndSProblem #6(a): Select Part (a) choices.(A) 20T (B) 17 (C) 67 (D) 237 (E) 13↑ Part (b) choices.Problem #6(b): SelectSaveT

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Answered: Let S be the portion of the plane 3x +…

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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Compute the flux of the vector field F⃗ =xi⃗ +3yj⃗ F→=xi→+3yj→ through the cylindrical surface shown below, if a=1a=1 and b=4b=4 and it is oriented away from the z-axis.
Find the flux of the field F = y2i + xzj - k outward (normal away from the z-axis) through the cone z = 22x2 + y2, 0<= z<= 2
Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the surface S surrounding the region D bounded by the planes y = 0, z = 0, z = 2 - y and the parabolic cylinder z = 1 - x2.
Compute the flux of the vector field F→=5xi→+yj→ through the cylindrical surface shown below, if a=2 and b=4 and it is oriented away from the z-axis.
Compute the flux of the vector field F = xi + 5yj through the cylindrical surface as shown in the image below, if radius a = 5 and height b = 7 and it is oriented away from the z axis.
5.Find the circulation of the field F(x, y, z) = (x-y)i+2yj around the circler(t) = costi+ sin tj , 0<=t<=2π
The flow of a gas with a density of d = 0.3 kg/m2 987 over the closed curve r(t) = (cos t)i + (sin t)j, 0<= t <= 2pai, is given by the vector field F = dv, where v = x2i - yj is a velocity field measured in meters per second. Find the flux of F across the curve r(t).
Compute the flux of the vector field F =2xi +3yj through the cylindrical surface shown below, if a=3 and b=8 and it is oriented away from the z-axis.
calc 3 13.7 #5 Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx kS is the part of the paraboloid z = 2 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientation.
Find the value of the line integral ∫CF→⋅dr→if F→(x,y)=(y^3+11)i→+(3xy+11)j→is a conservative vector field and Cis the semi circular path from (0,0)to (9,0)shown in the figure below.
Let Q be the solid region bounded by the surface S of equation given by z2 = x2 + y2 , 0 ≤ z ≤ 3, and the cylinder of equation x2 + y2 = 9,0 ≤ z ≤ 3.Find the outward flux of the vector field G(x, y, z) = x2 i+ y2 j+ z2 k through the surface S where S is the surface of Q.
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