Page 52 - Engineering Mathematics Workbook_Final

Calculus

8 2 1 1
)
I =   f ( , x y dydx leads to (a) 4 (b) 2
0 / 4
x
s q 1
)
I =   f ( , x y dxdy . What is q? (c) (d) 1
3
r p
316. The value of
2
(a) 4y (b) 16y (c) x (d)8 2 sin y
[GATE-2005] 0   x   0  dz dy dx =
y
1 x 2
311. The value of   e / y x dy dx = (a) -2 (b) 2
0 0
(c) -4 (d) 4
_________
[GATE]
[JNU]


 / 2 / 2 cos y
312. The value of   dydx = 317.   1 1 y 1 x dxdy = 3
+
0 x y 0 y
______ 2 2 1
−
(a) 2 2 (b)
[CSIR] 2

1 2 2 2 1 2 2 1
−
−
2
x
313. The value of   e dx dy = (c) (d)
0 2 y 8 9
__________ [IISC]
x
4
4
3
(a) e (b) e − 1 318. The integral 0  1 x  x 2 e − x y dy dx =
y
e − 1 e 4
4
(c) (d) ____
4 4
e − 2 e − 1
314. Let (a) (b)
e 2e
1 1 1 b
 xy sin xy  xy sin xydx dy e − 1 e − 1
( )dx dy =
0 y 0 a (c) 2 (d) 2e
then

(a) a = 0, b = x (b) a = 1, b = x 319. The volume enclosed by the surface
)
x
f ( ,x y = e over the triangle
x
(c) a = 0, b = 1 (d) a = − 1,b =
bounded by the lines
 
3
315.   x 4 .e − x y dx dy =__________ x = ; y x = 0; y = 1in the xy plane is
0 1/ 4
_________

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