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If ∫ 0 k d x 2 + 18 x 2 = π 24 , then the value of k is

Options

  1. A3
  2. B4
  3. C1 3
  4. D1 4

Correct answer

C. 1 3

Step-by-step solution

1 2 ∫ 0 k d x 1 + 9 x 2 = π 24 ⇒ ∫ 0 k d x 1 + ( 3 x ) 2 = π 12 ⇒ ( 1 3 tan − 1 ( 3 x ) ) 0 k = π 12 ⇒ tan − 1 3 k = π 4 ⇒ 3 k = 1 ⇒ k = 1 3

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