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Let g: R R be a differentiable function such that g(2)=-40 and g^ (2)=-5 then _ x 0 ( g (2-x^2 ) g(2) )^ 4 x^2 is equal to

Options

  1. Ae³²
  2. Be
  3. C1 e
  4. De ⁻⁵

Correct answer

C. 1 e

Step-by-step solution

aligned & _e^ _ x 4 x^2 [ lng (2-x^2 )- lng (2) ] ( 0 0 form ) & _ x 0 g^ (2-x^2 ) g (2-x^2 ) (-2 x) 2 x =e^ - g^ (2) g(2) =e^ - 1 2 = 1 e aligned

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