Integrals

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

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

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

4 01 ( 1 3 + x2 + 1 + x2 )dx - 3 e( 3) is equal to :

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

The integral 80 0 4 ( + 9 + 16 2 )d is equal to :

1. 3 4
2. 4 3
3. 6 43
4. 2 3

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

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

Let f: R R be a twice differentiable function such that f(2) = 1. If F(x) = x f(x) for all x R, 02 x F'(x) dx = 6 and 02 x2 F''(x) dx = 40, then F'(2) + 02 F(x) dx is equal to:

1. 13
2. 11
3. 9
4. 15

If f(x) = 1x1/4 (1 + x1/4 )dx, f(0) = -6, then f(1) is equal to :

1. 4 ( e 2 - 2 )
2. e2 2 + 2
3. 2 - e2
4. 4 ( e 2 + 2 )

Let f be a real valued continuous function defined on the positive real axis such that g(x) = 0x t f(t) dt. If g (x3 ) = x6 + x7, then value of r=115 f (r3 ) is :

1. 270
2. 340
3. 310
4. 320

If I(m,n)= 01xm-1(1-x)n-1dx, m,n>0, then I(9,14)+I(10,13) is

1. I(9,1)
2. I(1,13)
3. I(19,27)
4. I(9,13)

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

Let I(x)= dx(x-11) 1113(x+15) 1513. If I(37)-I(24)= 14 ( 1b 113- 1c 113 ), b,c N, then 3(b+c) is equal to

1. 39
2. 22
3. 40
4. 26

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

Let x3 x dx=g(x)+C, where C is the constant of integration. If 8 (g ( 2 )+g' ( 2 ) )= 3+ 2+ , , , Z, then + - equals :

1. 47
2. 55
3. 62
4. 48

Let for f(x)=7 8x+7 6x-3 4x-3 2x, I1= 0 /4f(x) dx and I2= 0 /4x f(x) dx. Then 7I1+12I2 is equal to :

1. 2
2. 1
4. 2

If x ( x -1x 1-x2+ -1x(1-x2)3/2+ x1-x2 )dx=g(x)+C, where C is the constant of integration, then g ( 12 ) equals :

1. 6 e3
2. 6 e2
3. 4 e3
4. 4 e2

Let 2 - x3 + x dx = 12 ( x + e| x + x| ) + C, where C is the constant of integration. Then + is equal to :

1. 3
2. 7
3. 1
4. 4

The integral 1/43/4 (2 -1 1 - x1 + x ) dx is equal to

1. -1/2
2. -1/4
3. 1/4
4. 1/2

x 2 ( x3( /2)3 ( (2t1/3 ) + (t1/3 ) ) dt (x - 2 )2 ) is equal to

1. 3 22
2. 9 28
3. 5 29
4. 11 210

The value of the integral -12 e (x + x2 + 1 ) dx is

1. 5 - 2 + e ( 7 + 4 51 + 2 )
2. 2 - 5 + e ( 7 + 4 51 + 2 )
3. 5 - 2 + e ( 9 + 4 51 + 2 )
4. 2 - 5 + e ( 9 + 4 51 + 2 )

The value of k N for which the integral In = 01 (1 - xk )n dx, n N, satisfies 147 I20 = 148 I21 is

1. 8
2. 14
3. 7
4. 10

Let I(x) = 6 2 x(1 - x)2 dx. If I(0) = 3, then I ( 12 ) is equal to

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

Let e 4 dx ex - 1 = 6. Then e and e- are the roots of the equation :

1. 2x2 - 5x + 2 = 0
2. x2 - 2x - 8 = 0
3. 2x2 - 5x - 2 = 0
4. x2 + 2x - 8 = 0

0 /4 2 x 2 x ( 3 x + 3 x )2dx is equal to

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

If 1a2 2 x + b2 2 x dx = 112 -1(3 x) + constant, then the maximum value of a x + b x, is :

1. 41
2. 39
3. 40
4. 42

The integral 0 /4 136 x3 x + 5 x dx is equal to :

1. 3 - 50 e 2 + 20 e 5
2. 3 - 25 e 2 + 10 e 5
3. 3 - 10 e(2 2) + 10 e 5
4. 3 - 30 e 2 + 20 e 5

The value of - 2y(1 + y)1 + 2 y dy is :

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

Let (m, n) = 01 xm - 1(1 - x)n - 1 dx, m, n > 0. If 01 (1 - x10 )20 dx = a (b, c), then 100(a + b + c) equals .

1. 2012
2. 1021
3. 1120
4. 2120

Let f(x)= cases-2, & -2 x 0 \ x-2, & 0<x 2 cases and h(x)=f(|x|)+|f(x)|. Then -22 h(x) dx is equal to:

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

If the value of the integral -11 x1 + 3x dx is 2 , then a value of is

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

The value of the integral 0 /4 x dx 4(2x)+ 4(2x) equals :

1. 2 28
2. 2 216
3. 2 232
4. 2 264