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Question

Let  f, f', f" be continuous in [0, ln 2] and f(0) = 0,  f'(0) = 3, f(In 2) = 6, f'(In 2) = 4 and  ln20e2xf(x)dx=3
 then ln20e2xf′′(x)dx  is
  1. 10
  2. 13
  3. 12
  4. None of these


Solution

The correct option is B 13
ln20e2xf′′(x)dx
=[e2xf(x)]ln20+2ln20e2xf(x)dx
=[14f(In2)3]+2[e2xf(x)+2e2xf(x)dx]In20=13

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