Qus : 3 1 If a < b ∫ b a ( | x − a | + | x − b | ) d x
1 ( b − a ) 2 2 2 b 2 − a 2 2 3 a 3 − b 3 2 4 ( b − a ) 2 Go to Discussion
Solution Qus : 4 2 Which of the following is TRUE?
A. If f [ a , b ] ∫ b a x f ( x ) d x = x ∫ b a f ( x ) d x
B. ∫ 3 0 e x 2 d x = ∫ 5 0 e x 2 d x + ∫ 5 3 e x 2 d x
C. If f [ a , b ] d d x ( ∫ b a f ( x ) d x ) = f ( x )
D. Both (a) and (b)
1 A 2 B 3 C 4 D Go to Discussion
Solution Qus : 5 2 If for non-zero x, c f ( x ) + d f ( 1 x ) = | log | x | | + 3 , c ≠ 0 ∫ e 1 f ( x ) d x =
1 ( c − d ) ( 2 e − 1 ) c 2 − d 2 2 ( c − d ) ( 3 e − 2 ) c 2 − d 2
3 ( c − d ) ( 3 e + 2 ) c 2 − d 2
4 ( c − d ) ( 2 e + 1 ) c 2 − d 2
Go to Discussion
Solution Qus : 9 3 The value of ∫ π / 4 0 l o g ( 1 + t a n x ) d x
1 π 4 l o g 2 2 π 6 l o g 2 3 π 8 l o g 2 4 π 2 l o g 2 Go to Discussion
Solution Qus : 10 2 If [x] represents the greatest integer not exceeding x, then ∫ 9 0 [ x ] d x
1 32 2 36 3 40 4 28 Go to Discussion
Solution Qus : 11 2 Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of
1 Circles 2 Parabolas 3 Hyperbolas 4 Straight Lines Go to Discussion Solution Qus : 12 1 The value of
is
1 π3 -6π 2 - π 3 - 6π 3 - π3 + 6π 4 π3 + 6π Go to Discussion
Solution Qus : 14 2 The value of ∫ π / 3 − π / 3 x s i n x c o s 2 x d x
1 1 3 ( 4 π + 1 )
2 4 π 3 − 2 l o g t a n 5 π 12
3 4 π 3 + l o g t a n 5 π 12
4 4 π 3 − l o g t a n 5 π 12
Go to Discussion
Solution Qus : 15 2 If
where
n is a positive
integer, then the relation between
In and
In-1 is
1 2 3 4 Go to Discussion
Solution Qus : 16 2 The value of
depends on the
1 Value of b 2 Value of c 3 Value of a 4 Value of a and b Go to Discussion
Solution Qus : 17 4 ∫ π 0 [ c o t x ] d x
1 π 2 2 1 3 -1 4 − π 2 Go to Discussion
Solution Qus : 18 2 The value of ∫ π / 3 − π / 3 x sin x cos 2 x d x
1 1 3 ( 4 π + 1 )
2 4 π 3 − 2 log tan 5 π 12
3 4 π 3 + log tan 5 π 12
4 4 π 3 − log tan 5 π 12
Go to Discussion
Solution [{"qus_id":"3782","year":"2018"},{"qus_id":"3793","year":"2018"},{"qus_id":"3756","year":"2018"},{"qus_id":"3757","year":"2018"},{"qus_id":"3938","year":"2019"},{"qus_id":"3917","year":"2019"},{"qus_id":"4305","year":"2017"},{"qus_id":"4309","year":"2017"},{"qus_id":"9455","year":"2020"},{"qus_id":"9456","year":"2020"},{"qus_id":"11117","year":"2022"},{"qus_id":"11510","year":"2023"},{"qus_id":"11633","year":"2024"},{"qus_id":"11638","year":"2024"},{"qus_id":"10197","year":"2015"},{"qus_id":"10228","year":"2015"},{"qus_id":"10444","year":"2014"},{"qus_id":"10446","year":"2014"}]
then x =
is equal to
be defined by 
. Find 
and 
, then the value of 
is
is
dx
where 
depends on the