Integrals

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 .

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

If f(t) = 0 2x dx1 - 2 t 2 x, 0 < t < , then the value of 0 2 2 dtf(t) equals .