Integrals · Question 24

Let I(x) = 3 dx(4x + 6) ( 4x2 + 8x + 3 ) and I(0) = 34 + 20. If I ( 12 ) = a 2b + c, where a, b, c N, (a, b) = 1, then a + b + c is equal to :

1. 30
2. 29
3. 28
4. 31

The number of elements in the set S = \x : x [0, 100] and 0x t2 (x - t) dt = x2 \ is

The value of - 2 2 ( 1[x] + 4 ) dx, where [ ] denotes the greatest integer function, is

1. 160(21 - 1)
2. 160( - 7)
3. 760( - 3)
4. 760(3 - 1)

If ( x) -112( x) -52 dx = - p1q1( x) 92 - p2q2( x) 52 - p3q3( x) 12 + p4q4( x) -32 + C, where pi and qi are positive integers with (pi, qi) = 1 for i = 1, 2, 3, 4 and C is the constant of integration, then 15p1p2p3p4q1q2q3q4 is equal to

Let [.] be the greatest integer function. If = 064 (x1/3 - [x1/3] )dx, then 1 0 ( 2 6 + 6 )d is equal to .

The value of - /6 /6 ( + 4x111 - (|x| + /6) )dx is equal to:

1. 8
2. 4
3. 2
4. 6

6 0 |( 3x + 2x + x)| dx is equal to .

Let [ ] denote the greatest integer function and f(x) = n 1n3 k=1n [ k23x ]. Then 12 j=1 f(j) is equal to .

If 01 4 -1 (1 - 2x + 4x2 )dx = a -1(2) - b e(5), where a, b N, then (2a + b) is equal to .

The integral -1 32 ( | 2 x ( x) | )dx is equal to:

1. 2 + 3
2. 4 +
3. 1 + 3
4. 3 + 2