Let F(x,y)=(:-y,x:) and C be the ellipse (x^2)/(16)+(y^2)/(9)=1 oriented counter clockwise, then find the value of int_C F.dr

Averi Fields 2022-09-25 Answered
Let F ( x , y ) = y , x and C be the ellipse x 2 16 + y 2 9 = 1 oriented counter clockwise, then find the value of C F . d r
This is how I tried it,
x = 4 cos ( t ) d x = 4 sin ( t )
y = 3 sin ( t ) d y = 3 cos ( t )
and 0 t 2 π
C F . d r = y d x + x d y = t = 0 2 π 12 ( sin 2 ( t ) + cos 2 ( t ) ) d t = 75.4
But answer given to me at the back is 98.2 and doesn't agrees with mine.
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Answers (1)

skarvama
Answered 2022-09-26 Author has 5 answers
Your solution is correct. In fact,
C F ( r ) d r = 0 2 π ( 3 sin t , 4 cos t ) ( 4 sin t , 3 cos t ) d t = 0 2 π 12 ( sin 2 t + cos 2 t ) d t = 24 π 75.3982
There is a typo/mistake in the book. It happens sometimes.
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