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AP EAMCET202023 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual

∫ - a a a - x a + x d x =

Options

  1. Aa π 2
  2. B1
  3. C2 aπ
  4. Daπ

Correct answer

D. aπ

Step-by-step solution

I = ∫ - a a a - x a + x d x f ( x ) ⇒ f ( a + b - x ) I = ∫ - a a a + x a - x d x ⇒ 2 I = ∫ - a a 2 a a 2 - x 2 d x I = 2 a ∫ 0 a d x a 2 - x 2 = 2 a sin - 1 x a 0 a = 2 a π 2

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