Exam 13: Extension D: Vector Calculus

A particle starts at the point ,moves along the x-axis to (3,0)and then along the semicircle to the starting point.Use Green's Theorem to find the work done on this particle by the force field

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. , where C is the boundary of the region bounded by the parabolas and

Let D be a region bounded by a simple closed path C in the xy.Then the coordinates of the centroid where A is the area of D. Find the centroid of the triangle with vertices (0,0),( ,0)and (0, ).

A plane lamina with constant density occupies a region in the xy-plane bounded by a simple closed path C.Its moments of inertia about the axes are Find the moments of inertia about the axes,if C is a rectangle with vertices (0,0),(4,0), (4,5)and

Use Green's Theorem to find the work done by the force in moving a particle from the origin along the x-axis to (1,0)then along the line segment to (0,1)and then back to the origin along the y-axis.

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. ,where C is the triangle with vertices , ,and