Let C be the curve consisting of the three line segments from (0,0) to (1, 1), from (1, 1) to (1, -1), and from (1,-1) to (0,0). Use Green's theorem to find the flux integral of F = x²i+x²j across C. Let C₁ be the curve that starts at (1, 1), ends at (0,0), and has the parameterization r(t) = (1 − t, 1 − t), where t = [0, 1]. Let C₂ be the curve that starts at (1,1), ends at (0,0), and has the parameterization r(t) = (1+ cost, sint), where t Є [½‚π]. An unknown vector field F satisfies curl(F) = x + y and set up a double integral equal to the circulation integral C₁ F.dr = 0. Use Green's theorem to F dr. Do not evaluate. C2

Let C be the curve consisting of the three line segments from (0, 0) to (1, 1), from (1, 1) to (1, −1), and from (1, −1) to (0, 0).                                                                                                                                                                                                                                                                                                                                                           Use Green’s theorem to find the flux integral of F = x^2i + x^2j across C.                                                                                                                                                                                                                                                                                                                                                                                Let C1 be the curve that starts at (1, 1), ends at (0, 0), and has the…

Compute the line integral

A bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 seconds. Where is the bee located at time t = 6 if [°r' (Use symbolic notation and fractions where needed.) r' (u) du = 0 location:

Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y = x² from the origin to the point (2, 4) using t as a parameter. r(t) = (b) Find the line integral of along the parabola y = x² from the origin to (2, 4).

Compute F · dr where F(x, y) = <2x+1,y> and C is the path traced by the line segment starting at (0, −1) and ending at (1, 0), followed by the half circle of radius one above the x-axis runningcounterclockwise from (1, 0) to (−1, 0).

Use the given transformation to evaluate the integral. Jn 6z + 3ydA, where R is the parallelogram with vertices (블,3), (풍, 플), (블, 플), (불,-3) z = (u+ v), y -(2u – v).