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JEE Main202324 Jan 2023Evening ShiftMathematicsDefinite IntegrationActual

∫ 3 2 4 3 3 4 48 9 - 4 x 2 d x is equal to

Options

  1. Aπ 3
  2. Bπ 2
  3. Cπ 6
  4. D2 π

Correct answer

D. 2 π

Step-by-step solution

Given integration is ∫ 3 2 4 3 3 4 48 9 - 4 x 2 d x We know that ∫ d x a 2 - x 2 = sin - 1 x a + C So, the equation can be re-written as ∫ 3 2 4 3 3 4 48 2 3 2 2 - x 2 d x = 48 2 × sin - 1 2 x 3 3 2 4 3 3 4 = 24 × sin - 1 2 3 × 3 3 4 - sin - 1 2 3 × 3 2 4 = 24 × sin - 1 3 2 - sin - 1 1 2 = 24 × π 3 - π 4 = 2 π

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