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)

The value of the integral 6 3 ( 4-cosec2 x 4 x )dx is :

1. 11 3
2. 16 3
3. 323 3
4. 643 3

Let (21-a+21+a ), f(a), (3a+3-a ) be in A.P. and be the minimum value of f(a). Then the value of the integral e( -1) e( ) dx (e2x-e-2x ) is :

1. 12 e ( 43 )
2. 14 e ( 43 )
3. 12 e ( 85 )
4. 14 e ( 85 )

Let f : [1, ) R be a differentiable function defined as f(x)= 1x f(t) dt +(1-x) ( e x-1 )+e. Then the value of f(f(1)) is :

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

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