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Definite Integration
Name: ………………............. Date: …………… Time: 40 Minutes. M.Marks:40
Attempt all questions. All questions are single option correct type (+4, -1)
6
1. The value of  max(| 2 | x ||,
6
4 | x |, 3)dx is

(A) 40 (B) 50
(C) 60 (D) 30


I3
 e (sin x) dx , then
x n
2. If In = is equal to
0
I1
(A) 3/5 (B) 1/5
(C) 1 (D) 2/5

2x
3 tan1
1  x 2 dx and given the following statements
3. Let I  
0
1  x2
(i) I can be evaluated by the substituting x = tan  only
2 tan1 x
3
(ii) I  
0
1  x2
dx

2 tan1 x   2 tan1 x
1 3
(iii) I  
0
1  x2
dx  
1
1  x2
dx

1 2
(iv) I  
36
Then which of the following is / are correct?
(A) (i) and (ii) (B) (i), (ii), (iii)
(C) (ii), (iii), (iv) (D) (iii), (iv)


4. If f()  2 and   f(x)  f ''(x) sin x dx  5
0
then f(0) is equal to, (it given that f(x) is continuous in

[0, ])
(A) 7 (B) 3 (C) 5 (D) 1

5. Let f(x) is a continuous function for all real values of x and satisfies
x 1
x16 x 6

0 x

f(t)dt  t 2 .f(t)dt 
8

3
 a + a then value of ‘a’ is equal to

1 17 1
(A)  (B) (C) (D) None of these
24 168 7

x
et
6. f(x)  1
t
dt, x R . Then complete set of values of x for which f(x)  lnx is

(A) (0, 1] (B) [1, )

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 x
2t
7.  2  dt , where [.] denotes the greatest integer function, and x  R, is equal to
0
t

(A)
1
ln 2

[x]  2{x}  1  (B)
1
ln 2

[x]  2{x} 
(C)
1
ln 2

[x]  2{x}  (D)
1
ln 2

[x]  2{x}  1 
b
8. If f (a + b –x) = f (x) then  x f (x) dx is equal to
a

ab
b b
ab
(A)
2 
a
f (x) d x (B) 
 2 a 
 f (x) d x

(C) 0 (D) none of these

1 1 2 2
   
3 4 3 4
9. If 1  2x dx,  2  2x dx,  3  2 x dx and  4  2 x dx then
0 0 1 1
(A) 1  2 (B) 2  1
(C) 3   4 (D)  4   3 , 1   2

xm  ln x  dx 
1

n
10. m, n 
0
n m
(A) m, n1 (B) m, n1
n 1 n 1
n m
(C) m, n1 (D) m, n1
m 1 n 1

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Ph.: (Andheri : 42378100); (Chembur : 42704000); (Navi Mumbai : 41581500); (Thane : 41617777); (Kandivali : 32683438)
Web: www.fiitjee.com  email: academics.mumbai@fiitjee.com