Page 46 - Engineering Mathematics Workbook_Final

Calculus

3 2 5 2 4 4 16
(a) (b) (c) and 0 (d) and
512 256   

3 2 [GATE-17-CSIT]
(c)  ab (d) 0
256 270. The value of the integral

−
x
sin x
266. The value of  0  1 cos x dx =  −   / 4 1 cos2x dx is
+
2
2
  1 1
(a) (b) (a) 1− (b) 1−
−
4 2 2 2
 2  2
(c) (d) (c) 3− 1 (d) 2 − 1
4 8 2 2

267. Consider the following definite 271. The value of the integral
−
1
1 ( sin x ) 2
9
integral I =  dx .  dy is
−
0 1 x 2 0 y 1+ y
The value of the integral is
)
−
 3  3 (a) 4 (b) 4 ( 10 1
(a) (b)
24 12 (c) 8 (d) 12
 3  3
A
(c) (d) 272. Let ( ) t denote the area bounded by
48 64
x
the curve y = e , the x - axis and the
[GATE-17-CE] straight lines x = t − and x t , then
=
lim ( ) t is equal to
( )
2
t→
268. The value of  0  / 4 x cos x dx correct (a) 2 A (b) 1
to three decimal places (assuming (c) 1/2 (d) 0
that  = 3.14 ) is ____. 

1/ 2
273. e − y 3 .y dy =
[GATE-18-CSIT]
0
  x   
1
269. If ( ) x = R sin   + S , ' f   = 2 
f
 
  
 

2
 2    (a)  (b)
3
and  0 1 f ( ) x dx = 2R , then the constants 


(c)
2 (d) 0
R and S are respectively.
2 16 2 274. The value of  1 dt is ________
(a) and (b) and 0 0 − lnt
  

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