Page 21 - Engineering Mathematics Workbook_Final

Calculus

4 5 3
(a) (b) (c) (d) 0
3 4 4

5   x sin x 6
4
(c) (d) none of these 60. cos x dx =
3 0

56. Find the mean value ‘c’ of L.M.V.T for (a) 3 2 / 512 (b) 5 2 / 256
1/3
f x = (4 x ) in [1, 6] (c) 3 2 /128 (d) none of these
−
( ) 2 +
(a) 3 
61.  cos x dx = _____
−
(b) 4 0

(c) 8 62.  n   x dx = _____ , where [x] is a step
0
(d) cannot be applied function and ‘n’ is an integer.

8 ( n n + ) 1 ( n n − ) 1
f
1
57. If ( ) x = and f(0) = 1 (a) (b)
x + 2 3x + 4 2 2
then the lower and the upper bounds of f
(1) estimated by mean value theorem are (c) n (d) n + 1
2 2
5 1
(a) 2 and 3 (b) and 
6 10 2
)
63.  log (tan x dx =
3 4 0
(c) and (d) 7 and 5
4 3 
(a) 0 (b)
Definite Integrals 2

1  1 x  (c) (d) 
+
x
58.  2 cos log       dx = ____ 4
−
− 1  1 x 
2 d   e sin x
64. Let   F ( ) x   = , x  0. If
(a) 0 (b) 1 dx x
 sin x  2
 4   2e  dx =   F ( ) k − F ( ) 1 then k
(c) (d) none of these 1  x 
2  
= ________
4
59.   sin x dx =  2 
−    x   u  
65. If  = log     then x + y =
  y   x  y
(a)  (b)
2

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