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MHT CET202410 May 2024Evening ShiftMathematicsDefinite IntegrationActual

₀^2 x- a x+ a d x=

Options

  1. Aa -2 a 2
  2. Ba-a 2
  3. Ca +2 a 2
  4. Da+a 2

Correct answer

A. a -2 a 2

Step-by-step solution

aligned & Let I = ₀^ a x- a x+ a ~d x & Let x+ a = t & x= t - a & If x=0 , then t = a & If x= a , then t =2 a & ~d x= dt & I= _a^ 2 a t-2 a t d t & = _a^ 2 a 1 d t-2 a _a^ 2 a 1 t d t=[t]_a^ 2 a -2 a[ t]_a^ 2 a & = a -2 a ( 2 a - a ) & =a-2 a 2 aligned

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