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(Sections 15.1 and 15.2) Evaluate the following line integrals with respect to arc length
Z
L
x ds,
Z
−L
x ds,
Z
C
x ds.
Comment on your answers. (7)
(e) Evaluate the following line integrals:
Z
L
2xy dx + x
2dy,
Z
−L
2xy dx + x
2dy,
Z
C
2xy dx + x
2dy,
by
(i) transforming each integral to an ordinary single integral (see Section 15.3).
(ii) using the Fundamental Theorem of Line Integrals (Theorem 16.5.2) (12)
Hint for (ii)
• Let F (x, y) =
