Question

Use Green's theorem to evaluate the following integral where c is the triangle with vertices (0, 0), (9, 0), and (8, 5) (in the positive direction).

Answer 1

To evaluate the integral using Green's theorem, calculate the line integral along the boundary of the triangle and the double integral of the function over the region enclosed by the triangle.

Step-by-step explanation:

To evaluate the given integral using Green's theorem, we need to determine the line integral along the boundary of the triangle and the double integral of the function over the region enclosed by the triangle. The line integral can be evaluated by parameterizing the three sides of the triangle and integrating the dot product of the vector field and the tangent vector along each side. The double integral can be calculated by determining the partial derivatives of the vector field and setting up an iterated integral over the region.