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JEE Main2003MathematicsDefinite IntegrationActual

Let d d x F(x)= ( e^ sinx x ) x>0 . If ₁^4 3 x e^ sin ^3 d x=F(k)-F(1) then one of the possible values of k , is

Options

  1. A64
  2. B15
  3. C16
  4. D63

Correct answer

A. 64

Step-by-step solution

d d x F(x)= e^ x x or ₁^4 3 x e^ x^3 d x= ₁^4 3 x^2 x^3 e^ x^3 d x Let x ^3= t , 3 x ^2 dx = dt when x=1, t=1 & x-4, t=64 aligned & F ( t )= ₁⁶⁴ e ^ t t dt = ₁⁶⁴ ~F ( t ) dt = F (64)- F (1) & K =64 aligned

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