When I take the line integral around a square shape path "C" as follows:(adsbygoogle = window.adsbygoogle || []).push({});

From A to B to C to D to A

C1= A(0, 0) to B (4, 0)

ti

0 <= t <= 4

C2= B (4, 0) to C (4, 7)

4i+ (t - 4)j

4 <= t <= 11

C3= C (4, 7) to D (0, 7)

(15 - t)i+ 7j

11 <= t <= 15

C4= D (0, 7) to A (0, 0)

(22 - t)j

15 <= t <= 22

Why is that when I take the line integral around this path using [tex]\int_{C }||r'(t)|| dt[/tex] and the above parameterization, I end up with 0, when I should be getting the arc length of the path, which is the perimeter of the square?

Thanks!

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# Arc Length and Line Integrals

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