Use greens theorem to evaluate check the orientation

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Use Green's Theorem to evaluate (Check the orientation of the curve before applying the theorem.) Solution or Explanation and the region D enclosed by C is given by C is traversed clockwise, so − C gives the positive orientation. 3. 1/1 points | Previous Answers SCalcET7 16.4.018. A particle starts at the point moves along the x -axis to ( 2 , 0), and then along the semicircle to the starting point. Use Green's Theorem to find the work done on this particle by the force field Solution or Explanation Click to View Solution F · d r . C F ( x , y ) = y cos x xy sin x , xy + x cos x , C is the triangle from (0, 0) to (0, 6 ) to ( 2 , 0) to (0, 0) F ( x , y ) = y cos x xy sin x , xy + x cos x ( x , y ) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4 − 2 x . = − = − = − = − = − = − = = − 18 x 9 x 2 + x 3 = − 36 36 + 12 − 0 = −12 F · d r C ( y cos x xy sin x ) dx + ( xy + x cos x ) dy C ( xy + x cos x ) − ( y cos x xy sin x ) dA x y D ( y x sin x + cos x − cos x + x sin x ) dA D 2 0 y dy dx 6 3 x 0 y 2 dx 2 1 2 y = 6 3 x y = 0 0 ( 6 3 x ) 2 dx 2 1 2 0 18 18 x + x 2 dx 2 9 2 0 3 2 2 0 ( −2 , 0), y = 4 x 2 F ( x , y ) = 5 x , x 3 + 3 xy 2 .
13-11-18 HW #25 3/5 4. 1/1 points | Previous Answers SCalcET7 16.4.019.

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