Integrals

The value of the integral - /4 /4 ( 32 4 x1+e x )dx is :

1. 4 +2
2. 3 +8
3. 3 +4
4. 4 +3

The value of the integral -11 ( x3+|x|+1x2+2|x|+1 )dx is equal to :

1. 3 e 2
2. 2 e 2
3. 5 e 3
4. 3 e 3

The value of the integral 0 e(x)x2+4 dx is:

1. e(2)2
2. e(2)4
3. 1+ e(2)
4. 2+ e(2)

Let -22 (| x|+[x x] )dx=2(3- 2)+ , where [ ] is the greatest integer function. Then ( 2 ) equals:

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

If =1 and =1+i 2, where i= -1 are two roots of the equation x3+ax2+bx+c=0, a, b, c R, then -11 (x3+ax2+bx+c )dx is equal to :

1. -2
2. -4
3. -8
4. -10

The integral 01 -1 (1+x+x2 )dx is equal to :

1. 2 -12+ 12 e ( 54 )+ 2
2. 2 -12+ 12 e ( 54 )- 2
3. 2 -12- 12 e ( 54 )+ 2
4. 2 -12- 12 e ( 54 )- 2

Let [.] denote the greatest integer function. Then the value of 03 ( ex+e-x[x]! )dx is :

1. e2+e3- 1e2- 1e3
2. 12 (e2+e3- 1e2- 1e3 )
3. e2+e3- 12e2- 12e3
4. 12 (e2+e3 )- 1e2- 1e3

If = 02 3 2 (x2+4 )dx+ 24 2x-4 dx, then 2 is equal to .

The value of 020 ( 4 x+ 4 x )dx is equal to:

1. 15 2
2. 25
3. 15
4. 25 2

The value of r=120 ( | ( 0r x| x|dx ) | ) is .

Let [.] denote the greatest integer function. Then - 2 2 ( 12(3 + [x])3 + [ x] + [ x] ) dx is equal to :

1. 12 + 5
2. 11 + 2
3. 15 + 4
4. 13 + 1

If f(x) satisfies the relation f(x) = ex + 01 (y + xex) f(y) dy, then e + f(0) is equal to .

The value of the integral 24 5 24 dx1 + [3] 2x is :

1. 3
2. 18
3. 6
4. 12

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)

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 .

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

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

Let f(x) be a positive function and I1 = - 121 2x f(2x(1 - 2x)) dx and I2 = -12 f(x(1 - x)) dx. Then the value of I2I1 is equal to

1. 12
2. 9
3. 6
4. 4

The integral 0 (x+3) x1+3 2 x dx is equal to

1. 3( +1)
2. 3 3( +6)
3. 3( +2)
4. 2 3( +4)

The value of -11 (1 + |x| - x ) ex + ( |x| - x ) e-xex + e-x dx is equal to

1. 1 + 2 23
2. 1 - 2 23
3. 2 + 2 23
4. 3 - 2 23

Let the domain of the function f(x) = 2 4 6 (3 + 4x - x2) be (a, b). If 0b-a [x2] dx = p - q - r, p, q, r N, (p, q, r) = 1, where [ ] is the greatest integer function, then p + q + r is equal to

1. 10
2. 11
3. 9
4. 8

The integral 0 8x dx4 2 x + 2 x is equal to

1. 2 2
2. 4 2
3. 2
4. 3 22

Let [.] denote the greatest integer function. If 0e3 [ 1ex-1 ] dx = - e 2, then 3 is equal to .

Let (a, b) be the point of intersection of the curve x2 = 2y and the straight line y - 2x - 6 = 0 in the second quadrant. Then the integral I = ab 9x21 + 5x dx is equal to :

1. 27
2. 18
3. 24
4. 21

If 24 0 4 ( |4x- 12 |+[2 x] )dx=2 + , where [ ] denotes the greatest integer function, then is equal to .

If - 2 2 96x2 2 x(1 + ex) dx = ( 2 + ), , Z, then ( + )2 equals

1. 196
2. 100
3. 64
4. 144

The value of e2e4 1x ( e (( ex)2+1 )-1e (( ex)2+1 )-1+e ((6- ex)2+1 )-1 )dx is

1. 1
2. loge 2
3. e2
4. 2

If I= 0 2 32x 32x+ 32x dx, then 02I x x x 4x+ 4x dx equals :

1. 212
2. 24
3. 216
4. 28