I need some help on this question, it is from the book "The mathematical methods in the physical sciences".
7. Given v = x^2i + y^2j + z^2k
a. Integrating v*ndo for surface of the cube which its length is 1 and is consisted of 4 vertexes of (0,0,0), (0,0,1), (0,1,0), (1,0,0).
b. Using divergence theorem, calculate the above.
9. In 2-dimensional polar coordinate, find following answers by integrating.
a. In 1 quadrant, perimeter of the circle which its radius is a.
b. Area of circle which its radius ia a.
This in-depth solution shows step-by-step calculations on integration, divergence theorem and force fields.