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NDA2013MathematicsDefinite IntegrationActual

What is ₁^2 x d x equal to?

Options

  1. Aln 2
  2. B1
  3. C( 4 e )
  4. D( e 4 )

Correct answer

C. ( 4 e )

Step-by-step solution

I = ₁^2 (x) d x From integration by parts formula aligned & u= (x), v=1 & u v d x=u v d x- ( d u d x v d x ) d x = & x ₁^2 d x- ₁^2 ( d d x ( x) d x ) d x = & [ x (x)]₁^2- ₁^2 1 x x d x = & [x (x)-x]₁^2 = & 2 (2)-2-1 1+1 = & (2)^2-1 = & (4)- e= ( 4 e ) aligned

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