x
x
dx
e
+e−
∫
 is equal to
(A) tan–1 (ex) + C
(B) tan–1 (e–x) + C
(C) log (ex – e–x) + C
(D) log (ex + e–x) + C
42 2
(sincos2
cos )
x
dx
x
x
+
∫
 is equal to
(A)
–1
C
sin
cos
x
x
+
+
(B) log |sin
cos |
C
x
x
+
+
(C) log |sin
cos |
C
x
x
−
+
(D)
2
1
(sin
cos )
x
x
+
354
MATHEMATICS
43 If f (a + b – x) = f (x), then 
( )
b
∫a x f x dx
 is equal to
(A)
(
)
2
b
a
a
b
f b
x dx
+
−
∫
(B)
(
)
2
b
a
a
b
f b
x dx
+
+
∫
(C)
( )
2
b
a
b
a
− ∫f x dx
(D)
( )
2
b
a
a
b
f x dx
+ ∫
44 The value of 
1
1
2
0
2
1
tan
1
x
dx
x
x
−
−




+
−


∫
 is
(A) 1
(B) 0
(C) –1
(D)
4
π
Summary
� Integration is the inverse process of differentiation