2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C...
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)
solve the proplem using Maple 6. (a) Consider the line integral (2) dx+2y dy, where C is part of the ellipse 9r26y144 from the point (0,3) to the point o.-3). Plot the curve C and evaluate the line integral. (b) Consider the surface integralVi++i where S is the surface of the helicoid r(mu) =< u cost, u sin v, u >, integral 0 u 1, 0 u 2r. Plot the surface S and evaluate the surface 6. (a) Consider the...
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).
Evaluate the line integral Sc(xy? + siny)dx, where C is the arc of the parabola x=y2 from (0,0) to (12,n).
(3x{y4 – 6xy)dx + (4.x® y3 – 3x²)dy, where C is any path 13. Evaluate the line integral from (1, 2) to (2, 1). (a) 12 (6) 14 (c) 10 (d) – 10 (e) – 12 (1) -14 (g) – 16 (h) – 18
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.
please calculate directly, my answer is (3/2)pi+32/3 is that correct? (15%) Evaluate the line integral -r-y + ) dz+ (z+2cy+3)dy, where C consists of the arc Ci of the quarter circle +y 1,x 2 0,y 0, from (0,-1) to (1,0) followed by the arc C2 of the quarter ellipse 4z2y2 - 4, 2 0, y 20, from (1,0) to (0, 2) (15%) Evaluate the line integral -r-y + ) dz+ (z+2cy+3)dy, where C consists of the arc Ci of the...
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)
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...