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[answered] Calculus 3 (Math-UA-123) Fall 2016 Homework: Section 13.4 G


Could someone provide a detailed solution with explanation for Problems 2, problem 4, problem 13 and problem 14? I can find the solutions using calculators but I am confused in the actual way of solving it. Thanks a lot.


Calculus 3 (Math-UA-123) Fall 2016 Homework: Section 13.4

 

Give complete, well-written solutions to the following exercises.

 

1. Show that the value of I xy 2 dx + (x2 y + 2x) dy

 

C around any square depends only on the area of the square and not on its location in

 

the plane.

 

2. (a) For which of the following can you use Green?s Theorem to evaluate the integral?

 

Explain.

 

Z

 

I.

 

(x2 + y 2 )dx + (x2 + y 2 ) dy

 

C where C is the boundary of the region bounded by y = x, y = x2 , 0 x 1,

 

with

 

counterclockwise orientation.

 

Z

 

1

 

1

 

p

 

II.

 

dx p

 

dy

 

2

 

2

 

2

 

x +y

 

x + y2

 

C

 

where

 

C is the unit circle centered at the origin, oriented counterclockwise.

 

Z III. C F ? dr where F = xi + yj and C is the line segment from the origin to the point

 

(1, 1). (b) Use Green?s Theorem to evaluate the integrals in part (a) that can be done that

 

way. 1 1

 


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