Exam 15: Section 4: Vector Analysis

Use Green's Theorem to evaluate the line integral where C is the boundary of the region lying between the graphs of the circle and the ellipse .

Set up and evaluate a line integral to find the area of the region R bounded by the graph of .

Use Green's Theorem to calculate the work done by the force on a particle that is moving counterclockwise around the closed path C.

Evaluate , where is the unit circle given by .

Use Green's Theorem to evaluate the integral for the path C: boundary of the region lying between the graphs of and .

Use a computer algebra system and the result "The centroid of the region having area A bounded by the simple closed path C is " to find the centroid of the region bounded by the graphs of and .

Verify Green's Theorem by setting up and evaluating both integrals for the path C: square with vertices (0,0), (10,0), (10,10), (0,10).

Use Green's Theorem to evaluate the integral for C: boundary of the region lying between the graphs of and .

Use Green's Theorem to evaluate the integral for the path C: boundary of the region lying between the graphs of y = x and y = .

Use Green's Theorem to evaluate the line integral where C is .

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path C given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation . Round your answer to two decimal places.

Use Green's Theorem to evaluate the integral where C is the boundary of the region lying inside the rectangle bounded by and outside the square bounded by .

Find the maximum value of where C is any closed curve in the xy-plane, oriented counterclockwise.

Use Green's Theorem to calculate the work done by the force on a particle that is moving counterclockwise around the closed path C where C is the boundary of the region lying between the graphs of . Round your answer to two decimal places.

Use Green's Theorem to evaluate the integral for the path C: .

Verify Green's Theorem by evaluating both integrals for the path C defined as the boundary of the region lying between the graphs of and .

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path C given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation .

Use Green's Theorem to evaluate the integral for the path C defined as .