Do the following:
(1) Evaluate Int(P(x, y) dx + Q(x, y) dy) over the curve C, where P(x, y) = y^2, Q(x, y) = 3x, and C is the portion of the graph of the function y = 3x^2 from (-1, 3) to (2, 12). Here, "Int" stands for integral.
(2) Use the Divergence Theorem to evaluate the surface integral Int(F*n ds) over the surface S, where F = 3x i + 2y j + 4z k and S is the portion of the plane x + y + z = 6 that lies in the first octant. Here, "Int" stands for integral, F*n denotes the dot product of F and the unit vector n (the outward unit normal vector to S), and i, j, and k denote the unit vectors in the positive x, positive y, and positive z directions, respectively.© BrainMass Inc. brainmass.com October 24, 2018, 8:55 pm ad1c9bdddf
Complete, detailed solutions to both problems are provided in an attached .doc file (Calc1-WithSolutions.doc).
(1) The key step in solving problem 1 is to express every quantity in the integral in terms of the variable x (by using the fact that y = 3x^2 for every point on curve C), so that the ...
The given line integral and surface integral are evaluated, and a detailed explanation of each is provided.
As a Venezuelan business owner
Details: As a Venezuelan business owner (you may select the specific business of your choice), you are very interested in the fact that Venezuela has recently been accepted as an associate member of MERCOSUR (July, 2004). You need to prepare your operations in view of this new reality.
Develop a plan for your business that will be implemented as Venezuela becomes part of MERCOSUR. Your business plan should include the following:
Benefits and drawbacks for the country of Venezuela as a result of their membership in MERCOSUR.
Benefits and drawbacks for your business as a result of their membership in MERCOSUR.
What adjustments will need to be made to your business as a result of this?