If the integral I = ∫ 0 19 π d x 1 + e cos 3 ⁡ x has the value k π 2 , then k 2 is equal to

Question

If the integral I = ∫ 0 19 π d x 1 + e cos 3 ⁡ x has the value k π 2 , then k 2 is equal to,

MARKS App · Accepted Answer

Applying a + b - x and adding, 2 I = ∫ 0 19 π 1 1 + e cos 3 ⁡ x + 1 1 + e - cos 3 ⁡ x d x ⇒ 2 I = ∫ 0 19 π 1 d x = x 0 19 π ⇒ I = 19 π 2 ∴ k = 19 Hence, k 2 = 19 2 = 9.5

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