Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to (2,0,4). a. The line segment x = 2, y = 0, 0≤z≤4 b.The helix r(t) = (2cos t)i + (2sin t)j + c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola z = x², y = 0 from (0,0,0) to (2,0,4) b. Find The work done by F over the line segment is 3e4 +1. O A. B. C. df dt df dt df dt for F. = 1 //( 3 os ³t). + costsint+ 1 1/T 2t (2) ► = sint+ cost+ -e π k, 0≤t≤2 1 +7 ( sin ³t) + 2t 21/x - 21/x e π The work done by F over the helix is df 4t = cos ³t+2 costsint+ sin ³t+ 2e²1/7- dt 2t/x_2t/ e 2 + + df -= -8 cos ²t sint-4 sin ²t + 8 sin ²t cost + 4 cos dt 4t (2,0,4) 2t/x Z=X (2,0,0) (0,0,0)

Let F = (3y + 2) i + (4x – 22) 3 + (3r – y) k Find So FdF where C is a line segment 8. from A(2, –1,2) to B = (1, –1, 3).

What are coordinates of AABC with A(-4,3), B(3,1), and C(2,-5) after a reflection over the line y=x?

Find fe(x? + 3y)i + 3y³j) · dr where C consists of the three line segments from (2, 0, 0) to (2, 2, 0) to (0, 2,0) to (0, 2, 3). So((x² + 3y)i + 3y³j) · dr = 5/3