Use Green's Theorem to evaluate the line integral int_C(y+e^x)dx+(6x+cosy)dy where C is triangle with vertices (0,0),(0,2)and(2,2) oriented counterclockwise. a)6 b)10 c)14 d)4 e)8 f)12

Zoe Oneal

Zoe Oneal

Answered question

2021-03-12

Use Green's Theorem to evaluate the line integral

C(y+ex)dx+(6x+cosy)dy

where C is triangle with vertices (0,0), (0,2) and (2,2) oriented counterclockwise.

Answer & Explanation

toroztatG

toroztatG

Skilled2021-03-13Added 98 answers

Step 1
Given P=y+exandQ=6x+cosy
Green's theorem is
CPdx+Qdy=C(QxPy)dxdy
=C(61)dxdy
=5Cdxdy
Since C is closed triangle with vertices (0,0) , (0,2) and (2,2) which is oriented counter clockwise .
Since Cdxdy is the area of that triangle.
Step 2
Then
Cdxdy=1222=2
Hence
C(y+ex)dx+(6x+cosy)dy=5Cdxdy
=5×2=10
Therefore (2) option is correct.

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