(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.
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 ...
Solution Summary
The given line integral and surface integral are evaluated, and a detailed explanation of each is provided.
$2.19
See Also This Related BrainMass Solution
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?
... of merchandise and customs evaluation standards and ... Venezuela instrumenting today the strategic lines of an ... the block involved "giving the integration scheme a ...
... The bottom line for desirable aspect of fragmentation boils ... The integration of healthcare services is necessary to ... be done by in-depth evaluation and investing ...
... a classification of merchandise and customs evaluation standards and ... last, is Venezuela instrumenting today the strategic lines of an integration plan, or ...
... of merchandise and customs evaluation standards and ... Venezuela instrumenting today the strategic lines of an ... the block involved "giving the integration scheme a ...
... into psychological assessments and tests evaluations to decipher ... The integration of data and subsequent interpretations ... they form the introductory line to one ...
... as the gathering and integration of psychology ... Different tools of evaluation psychological tests among ... Admittedly, the line between what constitutes testing ...
... times it plugs up the condensate drain lines especially in ... Please provide a critical evaluation of this technology. ... cycle if temperature is an integral part of ...
... a pervasive sense of social integration where partners ... Taylor for inspiring this line of research. ... composite implicit and explicit evaluation the discrepancy ...
... By high school and college, the line between geography ... be increased and regional integration can be ... paper products) Develop objective evaluations regarding the ...
... on long-term change and comprehensive quality integration (eg, into ... and seven FTE service line-based consultants ...Evaluation of coronary artery bypass graft (CABG ...
