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(a) da dy rain (b) fofo y dy dz (c) f f (4- y²) dy dz pln 8 play (3)

(a) da dy rain (b) fofo y dy dz (c) f f (4- y²) dy dz pln 8 play (3)

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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Instruction: Show all your calculations. Engineering Mathematics IV Tutorial Sheet: VI (Double, Triple, and Line Integral) (b) (c) f (d) (e) f 1. Evaluate the following integrals. (a) dx dy 2. y dy dr (4- y²) dy dz + dy dz 3y dz dy Exercise I ²y dz dy. Exercise II (a) Let R be a rectangular region bounded by the lines z = -1, z = 2, y = 0, and y = 2. Find: (b) Let R be the region bounded by y= 2², and y=x+ 6. Sketch the region R and evaluate ff* dx dy. (c) Integrate the function f(x,y) = bounded by the lines y = x, y = 2x, x = 1, r = 2. Exercise III over the region in the first quadrant 3. Evaluate the following integrals. (a) So So 2² + y² + 2² dzdydz (b) dzdydz (c) Jo Jo Jo cos(p+q+r) dpdgdr Exercise IV 4.1 Evaluate the following line integrals of f along the given curve for the given interval. (a) f(x, y, z) = 32√√3x² + y² + 2², r(t) = (1,1,t), -1<t<1 r(t) = (t.t,t), 1<t<∞ x² + y² +2²¹ 4.2 Evaluate the line integral of f(2²y)dz + (x² − y²)dy along the path: (a) y = 3r² from (0,0) to (1,3) (b) y 3r from (0,0) to (1,3) (b) f(x, y, z)=
Transcribed Image Text:Instruction: Show all your calculations. Engineering Mathematics IV Tutorial Sheet: VI (Double, Triple, and Line Integral) (b) (c) f (d) (e) f 1. Evaluate the following integrals. (a) dx dy 2. y dy dr (4- y²) dy dz + dy dz 3y dz dy Exercise I ²y dz dy. Exercise II (a) Let R be a rectangular region bounded by the lines z = -1, z = 2, y = 0, and y = 2. Find: (b) Let R be the region bounded by y= 2², and y=x+ 6. Sketch the region R and evaluate ff* dx dy. (c) Integrate the function f(x,y) = bounded by the lines y = x, y = 2x, x = 1, r = 2. Exercise III over the region in the first quadrant 3. Evaluate the following integrals. (a) So So 2² + y² + 2² dzdydz (b) dzdydz (c) Jo Jo Jo cos(p+q+r) dpdgdr Exercise IV 4.1 Evaluate the following line integrals of f along the given curve for the given interval. (a) f(x, y, z) = 32√√3x² + y² + 2², r(t) = (1,1,t), -1<t<1 r(t) = (t.t,t), 1<t<∞ x² + y² +2²¹ 4.2 Evaluate the line integral of f(2²y)dz + (x² − y²)dy along the path: (a) y = 3r² from (0,0) to (1,3) (b) y 3r from (0,0) to (1,3) (b) f(x, y, z)=
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