If _ 0 ^ x f(t) d t=x+ _ x ^ 1 t f(t) d t then the value of f (1) is

Mathematics · JEE Advanced · NTA ExamsIntegral Calculus

If \(\int_{0}^{x} f(t) d t=x+\int_{x}^{1} t f(t) d t\) then the value of f (1) is
  1. 1/2
  2. 0
  3. 1
  4. –1/2

Answer

(D) –1/2

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