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MHT CET20192 May 2019Morning ShiftMathematicsIndefinite IntegrationActual

∫ x 2 - a 2 x d x = ________

Options

  1. Ax 2 - a 2 - a cos - 1 ⁡ a x + c
  2. Bx x 2 - a 2 - 1 a tan - 1 ⁡ x a + c
  3. Cx 2 - a 2 + a sec - 1 ⁡ x a + c
  4. Dx 2 - a 2 + 1 x sec - 1 ⁡ x + c

Correct answer

A. x 2 - a 2 - a cos - 1 ⁡ a x + c

Step-by-step solution

Let I = ∫ x 2 - a 2 x d x put x = a secθ ⁡ d x = a secθ ⁡ tanθ ⁡ a ∫ s e c 2 θ - 1 d θ = a t a n θ - θ + c ⇒ x 2 - a 2 - a s e c - 1 x a + c

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