Green's Theorem Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Use Green's theorem to evaluate the closed line integral where is the boundary of the square with vertices and traversed counterclockwise.

(2) Use Green's theorem to evaluate the closed line integral where is the boundary of the circle traversed clockwise.

(3) Use Green's theorem to evaluate the closed line integral where is the boundary of the triangle with vertices and traversed counterclockwise.

(4) Use Green's theorem to evaluate the closed line integral where is the boundary of the square with vertices and traversed clockwise.

(5) Use Green's theorem to evaluate a closed line integral that represents the area enclosed by the region defined by the curve

(6) Use Green's theorem to evaluate a closed line integral that represents the area enclosed by the region defined by the trapezoid with vertices and

(7) Evaluate the closed line integral where is any piecewise smooth Jordan curve enclosing the origin, traversed counterclockwise.

(8) Evaluate the closed line integral where is the boundary of the region between the -axis and the semicircle traversed counterclockwise (including the -axis).

(9) Evaluate where is any Jordan curve whose interior does not contain the point

(10) If is a Jordan curve, show that

where is the region enclosed by

(11) Suppose is continuously differentiable in a doubly-connected region and that

throughout How many distinct values of are there for the integral

where is a piecewise smooth Jordan curve in

Cite this as:
Greens Theorem Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/greens-theorem-homework.html