Page 72 - Engineering Mathematics Workbook_Final

Vector Calculus
)
( ))
( ))
(  xy + 2y + sin e x dx + ( x y + cos e y dy the straight line joining (0,0,0 to (1,1,1 )
2
2
C
is ____ is ________
(a) 0 (b) -2 (a) 0 (b) 1
(c) -4 (d) -8 (c) 2 (d) 3
118. Let D be the triangular region in R bounded 122. The value of ( 2x − ) y i − yz j − y zk ) .
(

2
2
by the y axis, the line Y = 1 and the line b = C
dr . Where C is the upper half of the
x. Let C be the boundary of the curve of the
2
2
2
region and C is oriented in counter surface of the sphere x + y + z = 1above
clockwise. Then the value of xy plane is ______
 ( x + 2sin x cos ) x dx + (4x + y 2 )dy is
2
2
C
(a)  (b) −
_____
(c) 2 (d) 0
(a) 1 (b) 2
123. The value of  . F dr where
(c) 4 (d) 8 C

+
F = yi + zj xk and C is the curve
+
119. The value of ( 2x +  2 y 2 ) dx dy , where C bounded by x = cos y = sin z = is ___


0
C
is the boundary of the region in first (a)  (b) −
−
quadrant bounded by y = 0, x = 0 and (c) 2 (d) 2
+
x + 2 y = 2 1 ______ 124. If r = xi + yj zk then  . r dr is___
C
2
(a) -1 (b) − (a) 0 (b) 1
3
(c) 2 (d) 3
2
(c) (d) 1 125. The value of  e dx + x 2ydy dz where C is
−
3 C
2
120. The value of  yzdx xzdy xydx where C the curve x + 2 y = 2 0 and z = is ___
+
+
C
)
)(
is the line segment (1,1,0 2,3,2 is _ (a) 0 (b) 1
(c)  (d) 2
(a) 0 (b) 7
126. The value of ( x +  2 y 2 ) dx + 3xy dy where
2
(c) 9 (d) 12 C
121. The work done of a moving particle in the C is the circle x + 2 y = 2 4 in xy plane is ___
force field F = 5x i + (xz y j− ) + 3zk along (a) 4 (b) 8
2

(c) 12 (d) 16

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