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If I n = ∫ 0 n π m a x sin ⁡ x , s i n - 1 sin ⁡ x d x , then I 2 + I 4 has the value λ π 2 2 ; where λ is

Correct answer

3

Step-by-step solution

max sin ⁡ x , s i n - 1 sin ⁡ x is sin – 1 ⁡ sin ⁡ x Hence, I n = n 1 2 ⋅ π π 2 = n π 2 4 (area of triangle) ∴ I 2 + I 4 = 6 π 2 4

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