Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec. 9] Lim Integrals 279
(/-axis;
b) the parabola OnA, the axis oi symmetry
of which is the
c) the parabola OpA, the axis of symmetry of which is the
x-axis;
d) the broken line e) the broken line
OBA\
OCA.
2313. J 2xydx ^x 2
OA
counterclockwise.
dy
(x+u)dx (x i/)dy
x* + y*
as in Problem 2312.
Fig. 103
2315. ^tfdx + x*dy, where C is the upper half of the ellipse
c
x^acost, y = bs\r\t traced clockwise.
2316. \ cosydxsmxdy taken along the segment AB of the
bisector of the second quadrantal angle, if the abscissa oi the
A is 2 and the ordinate of B is 2.
point
x!f(l' d
2317.
(f ^* dll}
a
lemmscate r* = rt
co$2(p
, where
C is the right-hand loop
traced counterclockwise.
ol the
2318. Evaluate the line integrals with respect to expressionswhich
are total differentials:
(2. 8)
a) ^ xdy -\-ydx,
( - 1 2)
(2, 1)
ydx
,
d) f
(1. 2)
(a. 4) (i. i)
b) J xdx + ydy, c) $
(O r 1) (0, 0)
xdy (along a path that does not intersect the