bise the Green's Theorem to evaluate the line integral(y + e√x ) d x + (₂x + cosy ²) dyfoCWhere C is the boundary of the region endosedby the parabolax ² and x = y²(Don't evaluate)y=

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Answered: Use the Green's Theorem to evaluate the…

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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Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. 8x + cos s-dy- (9y2 + arctan x?) dx, where C is the boundary of the square with vertices (3, 3), (5, 3), (5, 5), and (3, 5). $ 8x + cos - dy - (9y² + arctan x²) dx = D (Type an exact answer.)
Use Green's theorem to evaluate the line integral along the given positively oriented curve. yex dx + 2e* dy, C is the rectangle with vertices (0, 0), (5, 0), (5, 6), and (0, 6)
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. Jo yex dx + 2ex dy, C is the rectangle with vertices (0, 0), (3, 0), (3, 4), and (0,4)
Evaluate the line integral § (x − y) dx + (x + y) dy, where C is the circle with center the origin and radius 2, using two methods: (a) directly (b) using Green's Theorem
Construct a homogeneous transformation matrix that performs a rotation by 90-degrees around the y axis in Euclidian 3-space. Let C = cos(a) and S=sin(a) in your solution.
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xe-5x dx + (x* + 2x?y²) dy хе Cis the boundary of the region between the circles x2 + y2 = 9 and x2 + y2 = 25
Use Green's Theorem to evaluate the following integral et2 dx + (9x+5) dy Where C is the triangle with vertices (0, 0), (9, 0), and (8, 7) (in the positive direction).
Apply Green's theorem to evaluate the line integral f xydx – xydy, where C is the boundary of the region lying between the graphs of y = 2x and y = v2x oriented in the counterclockwise direction. %3D
5) Using Green's theorem, convert the line integral .(6y² dx + 2xdy) to a double integral, where C is the boundary of the square with vertices ±(2, 2) and ±(2, -2). ( do not evaluate the integral)
Consider the line integral I = rydy-y²dr where is the square cut from the first quadrant by the lines a 1 and y = 1. (i) Find the line integral (ii) Find the line integral using the circulation form of Green's Theorem. using the flux form of Green's Theorem.
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Use the Green's Theorem to evaluate the line integral ( Cy+e³x ) dx+ (2x + cosy³) dy Where C is the boundary of the region enclosed by the parabola y = x ² and x = y² (Don't evaluate)