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Q1 (a) Let C be the boundary of the region A formed by the curve xy = 1 and lines x=1,x=4 and y = (i) (ii) = 0. Sketch the closed region A, indicating clearly the boundary of the region. [4] Evaluate directly the integral ((x-xy)dx + (x²+2y)dy), where C is the anticlockwise path around the boundary of A. (iii) Evaluate the integral in (ii) using Green's Theorem. [8] [6] (b) Let C be the space curve defined parametrically by r(t)-[t-2, 3] where r = [x, y, z]. = Evaluate E dr = E(r(t)) r'(c) dt For F = [(x+2)e, e, x+2] between t₁ = 0 and t₂ = 1. E [7]

Q1 (a) Let C be the boundary of the region A formed by the curve xy = 1 and lines x=1,x=4 and y = (i) (ii) = 0. Sketch the closed region A, indicating clearly the boundary of the region. [4] Evaluate directly the integral ((x-xy)dx + (x²+2y)dy), where C is the anticlockwise path around the boundary of A. (iii) Evaluate the integral in (ii) using Green's Theorem. [8] [6] (b) Let C be the space curve defined parametrically by r(t)-[t-2, 3] where r = [x, y, z]. = Evaluate E dr = E(r(t)) r'(c) dt For F = [(x+2)e, e, x+2] between t₁ = 0 and t₂ = 1. E [7]

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q1 (a) Let C be the boundary of the region A formed by the curve xy = 1 and lines x=1,x=4 and y = (i) (ii) = 0. Sketch the closed region A, indicating clearly the boundary of the region. [4] Evaluate directly the integral ((x-xy)dx + (x²+2y)dy), where C is the anticlockwise path around the boundary of A. (iii) Evaluate the integral in (ii) using Green's Theorem. [8] [6] (b) Let C be the space curve defined parametrically by r(t)-[t-2, 3] where r = [x, y, z]. = Evaluate E dr = E(r(t)) r'(c) dt For F = [(x+2)e, e, x+2] between t₁ = 0 and t₂ = 1. E [7]
Transcribed Image Text:Q1 (a) Let C be the boundary of the region A formed by the curve xy = 1 and lines x=1,x=4 and y = (i) (ii) = 0. Sketch the closed region A, indicating clearly the boundary of the region. [4] Evaluate directly the integral ((x-xy)dx + (x²+2y)dy), where C is the anticlockwise path around the boundary of A. (iii) Evaluate the integral in (ii) using Green's Theorem. [8] [6] (b) Let C be the space curve defined parametrically by r(t)-[t-2, 3] where r = [x, y, z]. = Evaluate E dr = E(r(t)) r'(c) dt For F = [(x+2)e, e, x+2] between t₁ = 0 and t₂ = 1. E [7]
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