Chapter 16: Integrals and Vector Fields - Section 16.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux - Exercises 16.2 - Page 956: 28

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Given: $\int_C F \cdot T ds-\int_C F. dr=\int_C (x+y) dx +(x+y) dy$ Now, $\int_C (x+y) dx +(x+y) dy=\int_C (x+y) dx + \int_C (x+y) dy$ and $\int_0^{2\pi}(2 \cos t +2\sin t) (-2 \sin t dt ) +(2 \cos t +2\sin t) (2 \cos t dt ) =\int_{0}^{2\pi} (4) (\cos 2t) dt=0$