Problem 4 4 points Evaluate the line integral o F d r where F ( x , y ) F 1 ( x , y ) i F 2 ( x , y ) j with F 1 ( x , y ) ( x 3 y 3 ) and F 2 ( x , y ) ( x 3 y 3 ) along a closed path C as in the depicted below Hints There are two different calculation methods ( i ) Direct evaluation of the line integral and ( ii ) Use of Green's Theorem in the plane Both would be easier with the use of polar coordinate system for an ellipse and a proper setup for integration domain

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Question: Problem 4 [ 4 points ] Evaluate the line integral o F * d r where F ( x , y ) = F 1

Problem

4 [4

points

]

Evaluate the line integral

o_{}^{} F * d r

where

F (x, y) = F_{1} (x, y) i + F_{2} (x, y) j

with

F_{1} (x, y) = (x^{3} + y^{3})

and

F_{2} (x, y) = (x^{3} - y^{3})

along a closed path

C

as in the depicted below.

[

Hints

]

There are two different calculation methods:

(

)

Direct evaluation of the line integral; and

(

)

Use of Green's Theorem in the plane. Both would be easier with the use of polar coordinate system for an ellipse and a proper setup for integration domain.

Problem 4 [ 4 points ] Evaluate the line integral

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