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NDA2021MathematicsIndefinite IntegrationActual

If 1- 2 x d x=A x+B x+C , where 0 x 4 , then which one of the following is correct?

Options

  1. AA+B=0
  2. BA+B-2=0
  3. CA+B+2=0
  4. DA+B-1=0

Correct answer

A. A+B=0

Step-by-step solution

aligned & I = 1- ^2 x d x, 0 x 4 & = ^2 x-2 x x+ ^2 x d x & = ( x- x)^2 d x aligned (i.e. x- x 0 when 0 x 4 ) aligned & I =- ( x- x) d x= ( x- x) d x & I = x- x+c= A x+ B x+ c aligned Thus, A+B=1-1=0

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