Integrals

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 .

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 0 4 2x1+ x x dx= 1a e ( a3 )+ b 3, where a, b , then a+b is equal to .

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