Page 44 - Engineering Mathematics Workbook_Final

Calculus

1
246. If (c) 1+ + .....+ 1
h
1 y+
5
4
  4 dx dy =   1 dy dx +   ( ) g dy dx 2 n + 1
=
y= 0 x= 0 x= 0 y= 0 x= 4 y g ( ) x 1 1
, then the functions g(x) and h(x) are, (d) 1+ + .....+ n + 2 [CSIR]
2
respectively

(a) (x – 4) and 1 (b) (x + 4) and 1
 /4
(c) 1 and (x – 4) (d) 1 and (x + 4) 250.  log + )
(1 tan x dx
0
[JAM GP 2009]

(a) 0 (b) log 2
247. The surface area obtained by revolving 4

y = 2x , for x  0,2 , about y-axis is  
(c) log 2 (d) log 2
8 2
(a) 2 5 (b) 4 5
 /2
+
2
(c) 2 5 (d) 4 5 251.  (a 2 cos x b 2 sin 2 ) x dx =
0
[JAM CA 2009] 
2
(a) 0 (b) (a + b 2 )

=
248. If the line y mx, 0 x  2 is rotated 2


about the line y = − 1, then the area of (c) (a + b 2 ) (d) (a + b 2 )
2
2
the generated surface is 4 8
[JNU]
+
+
(a) 4 (1 m ) 1 m
252. Let ‘ f ’ be a real valued function of a
real variable defined as
+
+
4
(b) (1 m 2 ) 1 m f ( ) x = x −  , where   x denote the
x
+
2
(c) 4 ( 1+ m ) 1 m largest integer less than or equal to x
1.25
. The value of  f ( ) x dx _________
0.25
+
+
2
(d) 4 (1 m ) 1 m is (up to 2 decimal places).
[GATE-2018 (EE)]
[JAM CA 2007] 253.  2 1 x dx = ________
−

249. For n N , the value of 0
(a) 0 (b) -1
n 1− ( / x n ) n
 dx = (c) 1 (d) 2
−
0 n x e 1
+
254. The value of  e (1 ln x ) dx is
(a) 0 1 x 2
1 1 1 (a) 1 (b) 1/e
(b) 1+ + + .........+
2 3 n
(c) e (d) 0

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