Integrals

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

If 1 [5](x - 1)4(x + 3)6 dx = A ( x - 1 x + 3 )B + C, where C is the constant of integration, then the value of + + 20AB is .

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

Let rk = 01 (1 - x7 )k dx 01 (1 - x7 )k+1 dx, k N. Then the value of k=110 17 (rk - 1 ) is equal to .

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

Let [t] denote the largest integer less than or equal to t. If 03 ( [x2 ] + [ x22 ] )dx = a + b 2 - 3 - 5 + c 6 - 7, where a, b, c Z, then a + b + c is equal to .