If the value of the integral ∫ 0 1 2 x 2 1 - x 2 3 2 d x is k 6 , then k is equal to:

Question

If the value of the integral ∫ 0 1 2 x 2 1 - x 2 3 2 d x is k 6 , then k is equal to:, 2 3 + π, 2 3 - π, 3 2 + π, 3 2 - π

MARKS App · Accepted Answer

k 6 = ∫ 0 1 2 x 2 1 - x 2 3 2 d x Let x = sin θ ⇒ d x = cos θ d θ ⇒ k 6 = ∫ 0 π 6 sin 2 θ 1 - sin 2 θ 3 2 cos θ d θ ⇒ k 6 = ∫ 0 π 6 sin 2 θ cos 3 θ cos θ d θ ⇒ k 6 = ∫ 0 π 6 tan 2 θ d θ = ∫ 0 π 6 s e c 2 θ - 1 d θ ⇒ k 6 = tan θ - θ 0 π 6 = 1 3 - π 6 = 2 3 - π 6 ⇒ k = 2 3 - π

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