VITEEE 2016 Paper

Let I =

b

∫

a

x f (x) dx
Let a + b - x = z ⇒ - dx = dz
When x = a , z = b and when x = b , z = a
∴ I = -

a

∫

b

(a + b - z) f (z) dz
I = (a + b)

a

∫

b

f (x) dx -

b

∫

a

x f (x) dx
I = (a + b)

a

∫

b

f (x) dx - 1 ;
2I = (a + b)

b

∫

a

f (x) dx
I = (

a+b

2

)

b

∫

a

f (x) dx