Page 79 - Engineering Mathematics Workbook_Final

Vector Calculus

2
(a) 0 (b)
+
+
(a) 6  / 2 (b) 8  3
+
+
(c) 12  (d) 16 2 (c) 1 (d) 2 3
[GATE-19-EC] [GATE-10 (EC)]

164. The value of the line integral 166. Let
 F  r ds , where C is a circle of C = (  , x ) y  R 2 ,max  , x y = 1 

C
4 the value of line integral
radius units is _______. Here,
( ))
( ))
 (  xy + 2y + sin e x dx + ( x y + cos e y dy
2
2
$
F ( , x y = ) y i + $ 2x j and r is the C
is ________ [CSIR]
UNIT tangent vector on the curve C at
an arc length s from a reference point on  e y ( y )
+
$ $ 167. Let I = dx + e ln x x dy ,
the curve. i and j are the basis vectors C x
in the x-y Cartesian reference. In where C is the positive oriented
evaluating the line integral, the curve has boundary of the region enclosed by
to be traversed in the counter-clockwise y = 1 x , y = 2 and x = 1
2
+
direction. [GATE-16-ME-SET 3] 2 then the
value of I = _______

(a) 1 (b) 5
8 24

u r ur 7 3
$

165. If A = xya x + x 2 $ y a then  A dr (c) 24 (d) 8
over the path shown in the figure is
[GATE]

77