Practice questions of indefinite integration to make you roots strong. Integration has a large weightage in JEE. This document will be perfect for you even if you are not pursuing JEE but the questions are of high level.
NAME : .....................................................................................................................................................
JEE (Main + Advanced) 2024
JEE (Main + Advanced) 2024
ENTHUSIAST COURSE
ENTHUSIAST COURSE
ASSIGNMENT # B (INDEFINITE INTEGRATION) MATHEMATICS
One or more than one correct :
1. ò tan ( x - 1) tan 2x tan ( x + 1) dx is equal to (where 'C' is the integration constant)
cos ( x + 1) cos ( x - 1) sec ( x + 1) sec ( x - 1)
(A) log +C (B) log +C
cos 2x sec 2x
sin ( x + 1) sin ( x - 1) cosec ( x + 1) cosec ( x - 1)
(C) log +C (D) log +C
sin 2x cosec2x
(
d sin 2 q )
2. ò (1 - sin q) cos ( 3q ) is equal to-
2
p p
tan tan
æ pö 6
æ pö 6
cos q + cos ÷ cos q + cos ÷
2 ç 6 2 ç 6
(A) ln ç ÷ esec q + C (B) ln ç ÷ e cos q + C
3 ç cos q - cos p ÷ 3 ç cos q - cos p ÷
ç ÷ ç ÷
è 6ø è 6ø
p p
tan tan
æ pö 6 æ pö 6
ç cos q + cos ÷ ç cos q + cos ÷
2 6 2 6
(C) ln ç ÷ esec( p-q) + C (D) ln ç ÷ e cos( p-q) + C
3 ç cos q - cos p ÷ 3 ç cos q - cos p ÷
ç ÷ ç ÷
è 6ø è 6ø
(where C is constant of integration)
3z3 - 8z + 5
3. If ò (
dz = z 2 + az + 36 ) z 2 - 4z - 7 + bln z - 2 + z 2 - 4z - 7 + C , where a,b Î I and C is
z - 4z - 7
2
integration constant, then-
(A) a > b (B) a < b
(C) a + b = 117 (D) exactly one out of a or b is a prime number.
x 2 + 20
4. Let ò (x sin x + 5 cos x)2
dx = f (x) + tan x + C , f(0) = 0 where C denotes constant of integration. Then
which of the following is(are) correct ?
-p 2p
(A) f(0) = 1 (B) f(–p) = 0 (C) f( p) = (D) ƒ ( -2p ) =
5 5
2x 2 sec2 xdx æ pö æ pö
5. If ò (x sec 2 x - tan x)2 = f(x) + cot x + x + C, where C is constant of integration, then value of f ç ÷ -f çè - ÷ø
è 4ø 4
is equal to
p p p p
(A) (B) (C) (D)
2+ p 2-p 4-p 4+p
MATHEMATICS / ASSIGNMENT E-
, JEE (Main + Advanced) 2024
ENTHUSIAST COURSE
2 2-x 3
6. I=ò 3 dx = 3 ƒ2 ( x ) + c , then |ƒ '(1)| is equal to -
(2 - x)2 2+x 4
(A) 2 (B) 1 (C) 4 (D) 3
æ xö
7. The value of ò sin x log çè cot 2 ÷ø dx is -
x x x
(A) – cos x log cot – log sin + log sec + c
2 2 2
x x
(B) –sin x logcot + log tan + c
2 2
x x x
(C) – cos x log tan – log sin + log sec + c
2 2 2
æ xö æ xö
(D) – sin x log ç cot ÷ + cos x log ç tan ÷ + c
è 2ø è 2ø
æ ö
xç 1 1 - 2x 2 ÷
8. The value of integral ò ç
e + ÷ dx is equal to -
( )
2 5
ç 1+ x 1 + x2 ÷
è ø
æ ö æ ö
ç 1
x x ÷ ç 1 x ÷
(A) e ç + ÷+c (B) e x ç - ÷+c
(1 + x ) (1 + x )
2 2 3
ç 1+ x
2 2 3
÷ ç 1 + x ÷
è ø è ø
æ ö
ç 1 x ÷
ex ç + ÷+c
(C) (D) None of these
(1 + x )
2 2 5
ç 1 + x ÷
è ø
x (y - x 2 ) dx d
9. If y =
x
and ò (x 2 + y)(x + y2 ) = f (y) + c then dy ( f (y) ) for x = 1 is equal to -
x2 +
x
x2 + 2
x + ...¥
5 -1 5 +1 2- 5
(A) 1 (B) (C) (D)
2 2 2
dx 1 + x3 b c
10. If ò x 4 (1 + x 3 )2 = a ln
x 3
+ 3+
x 1 + x3
+ d , then (where d is arbitrary constant) -
1 1 1 2 -1 1
(A) a = , b = ,c = (B) a = ,b = , c =
3 3 3 3 3 3
2 -1 -1 2 1 -1
(C) a = ,b = , c = (D) a = ,b = ,c =
3 3 3 3 3 3
E- MATHEMATICS / ASSIGNMENT
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