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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If f(x)= ₁^x t 1+t d t , then

Options

  1. Af ( 1 x )=- ₁^x t t(1+t) d t
  2. Bf ( 1 x )= ₁^x t t(1+t) d t
  3. Cf(x)+f ( 1 x )=0
  4. Df(x)+f ( 1 x )= 1 2 ( x)^2

Correct answer

D. f(x)+f ( 1 x )= 1 2 ( x)^2

Step-by-step solution

f ( 1 x )= ₁^ 1 / x t (1+t) d t= ₁^x - u 1+u u -1 u^2 d u= ₁^x t t(1+t) d t Now, f(x)+f ( 1 x )= ₁^x t (1+t) (1+ 1 t ) d t= ₁^x t t d t= [ ( t)^2 2 ]₁^x= ( x)^2 2

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