10. Evaluate the line integral Sc xy2dx + xạy dy where is the portion of the...
Evaluate the line integral Sc(xy? + siny)dx, where C is the arc of the parabola x=y2 from (0,0) to (12,n).
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.
14. Use Green's theorem to evaluate the line integral Sc 2xy3dx + 4x2y2 dy where Cis the boundary of the triangular" region in the first quadrant enclosed by the x-axis, the line x-1, and the curve y=x3.
I 8. [6 points) Evaluate the line integral, dr where F(x, y) = 2xy i + (x2 - y2); and C is where is the are of the parabola y = z from (1,1) to (2,4). (Hint: You may view C as =2 y=?,ists 2.)
3. (12 points) Evaluate the line integral S y3dx + (x3 + 3xy2)dy , where C is the path from (0,0) to (1,1) along the graph y = x3 and from (1,1) to (0,0) along the graph of y=x.
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...
5. Consider Sc 2xydx + (x + y)dy, where C is the path moving from (0,0) to (1, 1) along the graph of y = x3 and from (1, 1) to (0,0) along the graph of y = x oriented in the counterclockwise direction. a) Calculate the line integral using Green's Theorem. b) Calculate the same line integral using definition.
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise. 12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
Evaluate the line integral Sc Fodr where C is given by the vector function (EJ=<t2, to, z> for ost 43 and (x, y, z)=(x+ya, xz, y+ z7.