Deck 13: Extension D: Vector Calculus

Question 1

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

A) + e
B) + e
C)
D)

Answer 1

Question 2

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

A) 0
B)
C)
D)
E)

Answer 2

Question 3

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

A)
B)
C)
D)

Answer 3

Question 4

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)
B)
C)
D)
E)

Question 5

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.

Question 6

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

A)
B)
C)
D)
E)