Integrals

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

Let n ( n n4 + 1 - 2n (n2 + 1 ) n4 + 1 . . + n n4 + 16 - 8n (n2 + 4 ) n4 + 16 + . . + n n4 + n4 - 2n n2 (n2 + n2 ) n4 + n4 ) be k, using only the principal values of the inverse trigonometric functions. Then k2 is equal to .

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