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MHT CET202415 May 2024Evening ShiftMathematicsDefinite IntegrationActual

₀^ 4 ^2 x (1+ x)(2+ x) d x=

Options

  1. A( 3 4 )
  2. B1 3 ( 4 3 )
  3. C( 4 3 )
  4. D1 4 ( 3 4 )

Correct answer

C. ( 4 3 )

Step-by-step solution

Put 1+ x= t ^2 x ~d x= dt When x=0, t =1 and when x= 4 , t =2 aligned & ₀^ / 4 ^2 x (1+ x)(2+ x) d x & = ₁^2 dt t (1+ t ) & = ₁^2 dt t - ₁^2 dt 1+ t & = [ t - _ (1+ t (1) ]₁^2 & = _ e 2- _ e 3+ _ e 2 & = _ e ( 4 3 ) aligned

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