Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2009MathematicsFunctionsActual

The value of ( _ x 0 (4^x-1 )^3 x^2 4 (1+3 x) ), is

Options

  1. A( 4 3 ( 4)^2 )
  2. B( 4 3 ( 4)^3 )
  3. C( 3 2 ( 4)^2 )
  4. D( 3 2 ( 4)^3 )

Correct answer

B. ( 4 3 ( 4)^3 )

Step-by-step solution

( aligned & _ x 0 (4^x-1 )^3 x^2 4 (1+3 x) & = _ x 0 (4^x-1 )^3 x^3 (x / 2)^2 x^2 / 4 3 x (1+3 x) 4 3 & = 4 3 ( _e 4 )^3 1 _e(e)= 4 3 ( _e 4 )^3 . aligned )

Practice Functions on Quantrex Academy →

More from Functions

Let [x] denote the greatest integer x . If f(x)=[x] and g(x)=|x| , then the value of f (g ( 8 5 ) )-g (f (- 8 5 ) ) is 2024Number of real solution of 5- ₂|x| =3- ₂|x| is equal to 2024f(x)= x [ 2 x ]+ 1 2 , where x is not an integral multiple of and [.] denotes the greatest integer function, is 2024The function f: R R defined by f(x)= x 1+x^2 is 2024If f: R R, g: R R are defined by f(x)=5 x-3, g(x)=x^2+3 , then g o f⁻¹(3) is equal to 2024The domain of the real valued function f(x)= 2 x^2-7 x+5 3 x^2-5 x-2 is 2024If a function f : R - l R - m defined by f(x)= x+3 x-2 is a bijection, then 3 l+2 m= 2024f(x)= x+ x, g(x)=x^2-1 , then g(f(x)) is invertible if 2024 Full Functions list All BITSAT PYQs