Page 40 - Engineering Mathematics Workbook_Final

Calculus

2
(a) 2 − (b) 2 − 2 (a) 2 (b) 1
1
(c) 2 2 (d) 2 + 2 (c) (d) 0
2
218. The value of the integral [JAM MA 2007]
tan x
0   /2 tan x + cot x dx is 223. The value of the integral

−
(a) / 6 (b) / 2 −    /4 1 cos2x dx is

(c) 0 (d) / 4 2
−
1   log x (a) 1− 1 (b) 1− 1
e
219. The integral dx 2 2
x
1 1
(a) converges to e (c) 3− 2 (d) 2 − 2
1
(b) converges to
e [JAM GP 2008]

(c) converges to 1 224. The value of the integral
 is
(d) diverges 9 dy
0 y 1+ y
 1 dx
220. The value of is
0 x (1 x− ) ( )
−
(a) 4 (b) 4 10 1
 (c) 8 (d) 12
(a) 0 (b)
2 [JAM CA 2012]
(c)  (d) 2
2
x
225. Area enclosed by the curves y = and
2n+
f
221. Let ( ) x = n sin 1 x cos x . Then the 2
n
value of y = 2x − 1 lying in the first quadrant
lim 0   /2 f ( ) x dx − 0   /2 ( lim f ( )) is
x dx
n→  n n→  n
(a) 1/6 (b) 1/4
is
(c) 1/2 (d) 1/3
(a) 1/2 (b) 0 [JAM CA 2005]
(c) -1/2 (d) −

2 xy
222. Let A(t) denote the area bounded by the 226. The value of 0  1 y  1 x e dx dy
curve y = e − x , the x-axis and the e + 2 e − 2
=
straight lines x = − t and x t . Then (a) 2 (b) 2
lim A ( ) t is equal to
t→ 

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