Page 17 - Engineering Mathematics Workbook_Final

Calculus

(c) differentiable once but not twice on    2    3 3 2
(0,3) (a)   +   (b)  +
 
 
 
 
 2   2  4
(d) twice differentiable on (0, 3)
3 2
[MS 2008] (c)  − (d) 0
4
28. The area of the region enclosed by the
2
curve y = x and x + y = 2 is [MS 2008]
_______

27
(a) 3 (b)
2 1 1
31. The value of   3 x + 3 1 dx dy =
9 0 y
(c) (d) 9
2 2 5/2 2

(a) (b) (2 3/2 − ) 1
[MS 2008] 3 3

2
)
)

−
−
29. Define ( , x y = f ) x + y 2 cos 2 (t + ) x dt . (c) 2 ( 2 1 (d) 2 ( 2 1
0 3
df
)
Then (0, y =__________ [IISC 2006]
dx
32. Let [x] denote the greatest integer
(a) 0 1   1  
( )
cos y 2 function. The value of 1  2   x  2    dx =
(b)
2 ____________

( )
cos y 2 (a) 1 + 1 − 1 (b) 1 + 1
2
( )
(c) + cos y 2 3 2 2 3 2
2
1 1 1 1 1
2
y +
( )
(d) cos 2 ( ) cos y 2 (c) + + (d) −
3 2 2 3 2
[IISC 2006] [IISC 2006]

3
30. If  x f ( ) t dt = x 2 sin x + x , then 33. The area of the region bounded by
3
y
2 0 and y = is
0 y = x , x + − = 0
   ________
f       is _________
 2  (a) 0.25 (b) 0.50
(c) 0.75 (d) 1.0

15