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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If f(x)= ₀^4 e^ |t-x| d t(0 x 4) , the maximum value of f(x) is

Options

  1. Ae ^4-1
  2. B2 ( e ^2-1 )
  3. Ce ^2-1
  4. Dnone of these

Correct answer

A. e ^4-1

Step-by-step solution

aligned & f(x)= ₀^x e^ |t-x| d t+ _x^4 e^ |t-x| d t= ₀^x e^ x-t d t+ _x^4 e^ t-x d t=- .e^ x-t |₀ ^x+ .e^ t-x |_x ^4=e^x+e^ 4-x -2 & f^ (x)=e^x-e^ 4-x =0 x=4-x x=2 & f(0)=f(4)=e^4-1, f(2)=2 (e^2-1 ) , so maximum value of f(x) is e^4-1 aligned

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