Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5y³dx + 2x²dy, where Cis the square with vertices (0, 0), (1, 0), (1, 1), and (0, 1) oriented counterclockwise. 5y²dx + 2x²dy = i

Q: 14. Convert ₁ to Scalar Form. Determine how ₁ and π2 intersect. x = 6+2s T₁: y = 3s + 2t and ₂: 3x -…

A:

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

A:

Q: Z is a complex variable, z=x+iy question attached in photo

A: To calculate theline  integral over different paths

Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

A:

Q: Compute22-2 dz, where C is the square with vertices 2+2i, -2+2i, -2- 2i, and 2 - 2i oriented in the…

A: 1.Cauchy Residue Theorem:∫Cf(z)dz= 2πi[sum of Residues of f(z) at poles lies inside of the closed…

Q: (c) Find the flux of F through S. Show your work, and circle your final answer. (Note: This exercise…

A: c) Given the field equation, F=-9zi+xexz-2xex2j+12k The surface S is the portion of the plane…

Q: Can Stokes' Theorem be used to find the flux of F through S? Clearly answer yes or no, and then…

A: Given, F→=-9z,xexz-2xex2,12 and S is the portion of the plane 2x+3z=6 that lies in the first octant…

Q: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4 represent in…

A: Given: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4…

Q: Find the scalar triple product u.(v x w) if u = 3i - 2j - 5k; v = i + 4j - 4k; and w = 3j + 2k. And…

A:

Q: Use the transformation u = y - x, v = y, to evaluate the integral on the parallelogram R of vertices…

A:

Q: Find the rectangular form of 7T 3√/2e² i.e. the a + bi form. Do not include any spaces.

A:

Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

A: