∫ a b x x + a + b - x d x =.........

Question

∫ a b x x + a + b - x d x =........., a + b, b - a 2, a - b, a - b 2

MARKS App · Accepted Answer

Let l = ∫ a b x a x + a + b - x d x ….(i) l = ∫ a b a + b - x a + b - x + a + b - a + b - x l = ∫ a b a + b - x a + b - x + x ….(ii) On adding Eqs. (i) and (ii), we get 2 l = ∫ a b x + a + b - x x + a + b - x d x ⇒ 2 l = ∫ a b d x = x a b = b - a ⇒ l = b - a 2

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