(a) Show that the line integral C y sin x dx cos x dy isindependent of the path.(b)
Chapter 15, Problem 8(choose chapter or problem)
(a) Show that the line integral \(\int_{c} y \sin x d x-\cos x d y\) is independent of the path.
(b) Evaluate the integral in part (a) along the line segment from \((0, 1)\) to \((π,−1)\).
(c) Evaluate the integral \(\int_{(0,1)}^{(\pi,-1)} y \sin x d x-\cos x d y\) using Theorem 15.3.1, and confirm that the value is the same as that obtained in part (b).
Equation Transcription:
(0,1) (
Text Transcription:
integral_c y sin x dx - cos x dy
(0,1) (pi, -1)
integral_(0,1) ^(pi, -1) y sin x dx - cos x dy
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