Evaluate the line integral Sc(xy? + siny)dx, where C is the arc of the parabola x=y2...
Consider the line integral Sc xy dx + (x - y) dy where is the line segment from (4, 3) to (3,0). Find an appropriate parameterization for the curve and use it to write the integral in terms of your parameter. Do not evaluate the integral.
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
10. Evaluate the line integral Sc xy2dx + xạy dy where is the portion of the parabola y = x2 from (0,0) to (2,4).
Use Green's theorem to evaluate the line integral Sc xay dx + 2xy?dx where C is the triangle with vertices 10,0), 12, 2), and 12,8).
Evaluate the line integral «+xy+y)ds where C is the path of the arc along the circle given by x2 + y2 = 9, starting at the point (3,0) going counterclockwise making an inscribed angle of a The line integral equals (45-72*sqrt(2))/8 Submit Answer Incorrect. Tries 1/8 Previous Tries
2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C from (0,0) to (3,0), the path C2 from (3,0) to (2,1), and the path C3 from (2,1) to (0,0) by applying the following steps. (a) Evaluate (x + 2y) dx + c'dy, by parametrizing C C (b) Evaluate [ (x + 2y)dx + x>dy, by parametrizing C, (c) Evaluate | (x + 2y)dx + x’dy, by parametrizing C3 (d) Evaluate (+2y)dx + xºdy
find the average value of the following function Evaluate the following line integral along each path C--G is the line segment from (-5,-3) to (0,2). C Gis the arc ofthe parabola x-4-y2from (-5,-3)to (0,2) a. b. from (5,- 3) (12 points)|y'dx+ xdy Evaluate the following line integral along each path C--G is the line segment from (-5,-3) to (0,2). C Gis the arc ofthe parabola x-4-y2from (-5,-3)to (0,2) a. b. from (5,- 3) (12 points)|y'dx+ xdy
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where C is the triangle with vertices (0,0), (1,0) y (1,2)
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3) 5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)