Integrals · Question 15

Let f be a polynomial function such that f(x2 + 1) = x4 + 5x2 + 2, for all x R. Then 03 f(x) dx is equal to

1. 332
2. 53
3. 272
4. 413

If ( 1 - 5 2 x 5 x 2 x )dx = f(x) + C, where C is the constant of integration, then f ( 6 ) - f ( 4 ) is equal to

1. 1 3(26 - 3)
2. 4 3(8 - 6)
3. 1 3(26 + 3)
4. 2 3(4 + 6)

The value of r=120 ( | ( 0r x| x|dx ) | ) is .

Let f(x) = dxx2/3 + 2x1/2, be such that f(0) = -26 + 24 e(2). If f(1) = a + b e(3), where a, b Z, then a + b is equal to :

1. -5
2. -11
3. -18
4. -26

Let [.] denote the greatest integer function. Then - 2 2 ( 12(3 + [x])3 + [ x] + [ x] ) dx is equal to :

1. 12 + 5
2. 11 + 2
3. 15 + 4
4. 13 + 1

Let f(t) = ( 1 - ( e t)1 - ( e t) ) dt, t > 1. If f (e /2 ) = -e /2 and f (e /4 ) = e /4, then equals

1. 1 + 2
2. -1 - 2 2
3. -1 - 2
4. -1 + 2

If f(x) satisfies the relation f(x) = ex + 01 (y + xex) f(y) dy, then e + f(0) is equal to .

Let f(x) = (2 - x2 ) ex ( 1 + x )(1 - x)3/2 dx. If f(0) = 0, then f ( 12 ) is equal to:

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

The value of the integral 24 5 24 dx1 + [3] 2x is :

1. 3
2. 18
3. 6
4. 12

Let I(x) = 3 dx(4x + 6) ( 4x2 + 8x + 3 ) and I(0) = 34 + 20. If I ( 12 ) = a 2b + c, where a, b, c N, (a, b) = 1, then a + b + c is equal to :

1. 30
2. 29
3. 28
4. 31