Find the circulation and flux of the field fequalsminus4yiplus4xj around and across the closed semicircular path that consists of the semicircular arch bold r 1 (t )equals(nothingpcosine t)iplus(nothingpsine t)j, 0less than or equalstless than or equalspi, followed by the line segment bold r 2 (t )equalsnothingti, minuspless than or equalstless than or equalsp.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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