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1) Use Green's Theorem to calculate the work done by the force field F(x, y) = 5x²yi- 2x j on a particle that moves around the curve C bounded by y =-x'+10 and y =-4x+13 in C. the counter-clockwise direction. Sketch the curve 92 ans : Verify Green's Theorem in plane for f(a-2xy)dx + (x°y + 3)dy where C is the 2) 128) boundary of the region defined by y2 = 8x and x = 2. Sketch the curve C. ans:- 5 A curve Cis the boundary of a shaded region D which defined by y = 2x² - 4 and y = 2x in counter-clockwise orientation. Sketch the curve C, hence by using Green's theorem, evaluate the integral [e* – y* )dx + (2x² + 3)dy. (ans:3.6) 3) 4) Evaluate the integral ((2e" - 2x) dy + (2xy +1)dx using Green's theorem where C is consists of y = 4- x and straight line from (-2,0) to (2,0). Sketch the curve C. 64 ans:- 3 5) Evaluate the integral f(e* - y)dx + (sin y + x)dy using Green's theorem where C is 16 bounded by y = x -1 and y =1-x. Sketch the curve C. ans:- 6) The work of a particle moving counter-clockwise around the vertices (2,0), (–2,0) and 3e' (2,–3) with F: 2y, 2x - Vy +3 ) is given by W = F dr Using |cosx+ In x Green's theorem, construct the diagram of the identified shape, then find W. (ans:24) 7) Verify the Green's theorem for integral g. x²y dx + xy dy, where C is the boundary described counter-clockwise of a triangle with vertices A=(0,0), B=(0,3) and C=(-2,3) (ans: 4) 8) Next page

1) Use Green's Theorem to calculate the work done by the force field F(x, y) = 5x²yi- 2x j on a particle that moves around the curve C bounded by y =-x'+10 and y =-4x+13 in C. the counter-clockwise direction. Sketch the curve 92 ans : Verify Green's Theorem in plane for f(a-2xy)dx + (x°y + 3)dy where C is the 2) 128) boundary of the region defined by y2 = 8x and x = 2. Sketch the curve C. ans:- 5 A curve Cis the boundary of a shaded region D which defined by y = 2x² - 4 and y = 2x in counter-clockwise orientation. Sketch the curve C, hence by using Green's theorem, evaluate the integral [e* – y* )dx + (2x² + 3)dy. (ans:3.6) 3) 4) Evaluate the integral ((2e" - 2x) dy + (2xy +1)dx using Green's theorem where C is consists of y = 4- x and straight line from (-2,0) to (2,0). Sketch the curve C. 64 ans:- 3 5) Evaluate the integral f(e* - y)dx + (sin y + x)dy using Green's theorem where C is 16 bounded by y = x -1 and y =1-x. Sketch the curve C. ans:- 6) The work of a particle moving counter-clockwise around the vertices (2,0), (–2,0) and 3e' (2,–3) with F: 2y, 2x - Vy +3 ) is given by W = F dr Using |cosx+ In x Green's theorem, construct the diagram of the identified shape, then find W. (ans:24) 7) Verify the Green's theorem for integral g. x²y dx + xy dy, where C is the boundary described counter-clockwise of a triangle with vertices A=(0,0), B=(0,3) and C=(-2,3) (ans: 4) 8) Next page

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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1) Use Green's Theorem to calculate the work done by the force field F(x, y) = 5x²yi– 2x j on a particle that moves around the curve Cbounded by y =-x²+10 and y = -4x+13in the counter-clockwise direction. Sketch the curve C. 92 ans : 2) Verify Green's Theorem in plane for [(x - 2.xyxdx + (x²y+3)dy where C is the 128 boundary of the region defined by y² = 8x and x = 2. Sketch the curve C. ans:- 5 A curve Cis the boundary of a shaded region D which defined by y = 2x² – 4 and y = 2x in counter-clockwise orientation. Sketch the curve C, hence by using Green's theorem, evaluate the integral f(e* – y² ) dx + (2x² + 3)dy . (ans:3.6) 3) 4) Evaluate the integral [(2e" – 2x) dy + (2xy² +1)dx using Green's theorem where C is consists of y = 4-x and straight line from (-2,0) to (2,0). Sketch the curve C. 64 ans: 3 5) Evaluate the integral f(e* – y)dx+ (sin y + x)dy using Green's theorem where C is 16 bounded by y = x² -1 and y =1-x². Sketch the curve C. ans:- 6) The work of a particle moving counter-clockwise around the vertices (2,0), (–2,0) and 3e" (2, –3) with F =1 - 2y, 2x – Jy² +3 ) is given by W = o F•dr Using |cos x + In x Green's theorem, construct the diagram of the identified shape, then find W. (ans:24) 7) Verify the Green's theorem for integral g. x²y dx + xy dy, where C is the boundary described counter-clockwise of a triangle with vertices A= (0,0), B=(0,3) and C=(-2,3) (ans: 4) 8) Next page
Transcribed Image Text:1) Use Green's Theorem to calculate the work done by the force field F(x, y) = 5x²yi– 2x j on a particle that moves around the curve Cbounded by y =-x²+10 and y = -4x+13in the counter-clockwise direction. Sketch the curve C. 92 ans : 2) Verify Green's Theorem in plane for [(x - 2.xyxdx + (x²y+3)dy where C is the 128 boundary of the region defined by y² = 8x and x = 2. Sketch the curve C. ans:- 5 A curve Cis the boundary of a shaded region D which defined by y = 2x² – 4 and y = 2x in counter-clockwise orientation. Sketch the curve C, hence by using Green's theorem, evaluate the integral f(e* – y² ) dx + (2x² + 3)dy . (ans:3.6) 3) 4) Evaluate the integral [(2e" – 2x) dy + (2xy² +1)dx using Green's theorem where C is consists of y = 4-x and straight line from (-2,0) to (2,0). Sketch the curve C. 64 ans: 3 5) Evaluate the integral f(e* – y)dx+ (sin y + x)dy using Green's theorem where C is 16 bounded by y = x² -1 and y =1-x². Sketch the curve C. ans:- 6) The work of a particle moving counter-clockwise around the vertices (2,0), (–2,0) and 3e" (2, –3) with F =1 - 2y, 2x – Jy² +3 ) is given by W = o F•dr Using |cos x + In x Green's theorem, construct the diagram of the identified shape, then find W. (ans:24) 7) Verify the Green's theorem for integral g. x²y dx + xy dy, where C is the boundary described counter-clockwise of a triangle with vertices A= (0,0), B=(0,3) and C=(-2,3) (ans: 4) 8) Next page
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