Use Green's Theorem to evaluateF dr. (Check the orientation of the curve before applying the theorem.)F(x, y) = (y – In(x? + y²), 2 tan-1y/x)C is the circle (x – 1)2 + (y – 4)2 = 9 oriented counterclockwise

Answered: Use Green's Theorem to evaluate F dr.…

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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Similar questions

Sketch the curve given in parametric form by r = ti+ sin tj + cos tk, 0 < t < 2π, and write down an integral to determine its length. Calculate the length of this curve. Write down a simple algebraic relation that determines a simple surface on which the curve lies. The length of this curve is: (a) 2π√2 (b) 2π (c) 2√2 (d) π/2√√2 The surface on which the curve lies is: (i) a sphere x² + y²+z² = 1 (ii) a cylinder x² + y² = 1 (iii) an elliptic cylinder (3x)2 + y² = 1 (iv) a cylinder y²+z² = 1 22
Answer all parts
4.) Sketch the curve r = 1 + 5 sin by first sketching the graph of r as a function of in cartesian coordinates. Show work. (table) Note: requires two graphs.
Q2:Is the point lies on the curve? x² cos y- sin y = 0, (0, m) il so, Gind the eyuations of lines thut ure (a) tangeat und (b) norual to the curve at the given point.
2/F F. dr. (Check the orientation of the curve before applying the theorem.) Use Green's Theorem to evaluate F(x, y) = (y - cos(y), x sin(y)), C is the circle (x − 3)² + (y + 5)² = 16 oriented clockwise -
So F. dr. (Check the orientation of the curve before applying the theorem.) C F(x, y) = (y - cos(y), x sin(y)), C is the circle (x − 7)² + (y + 9)² = 9 oriented clockwise Use Green's Theorem to evaluate
Graph the line that is described parametrically by (x, y) (2t,5 t), then.. %3D (a) Confirm that the point corresponding to t = O is exactly 5 units from (3,9). (b) Write a formula in terms of t for the distance from (3,9)to (2t, 5- t). (c) Find the other point on the line that is 5 units from (3,9). (d) Find the point on the line that minimizes the distance to (3,9). You may want a calculator.
Suppose that a parametric curve is given by x = f(t), y = g(t) for 0 ≤ t ≤ 1. If f 0 (t) > 0, explain why we may express the curve as the graph of a function y = h(x) for some function h(x).
Using the graphing software application of your choice, plot the following: (a) The 3D plot of z = sin (xy). (b) The parametric plot of (t² + 3t, t³ − 1) for -5 ≤ t ≤ 5. -
Q3 What symmetries do these curves have?? r2 = 1- sin 0

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Use Green's Theorem to evaluate F dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = (y- In(x? + y?), 2 tan-1 y/x) C is the circle (x - 1)2 + (y – 4)² = 9 oriented counterclockwise