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

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Question: Answered & Verified by Expert

If

I_{n} = \int_{0}^{n π} m a x (|\sin x|, |s i n^{- 1} (\sin x)|) d x

, then

I_{2} + I_{4}

has the value

\frac{λ π^{2}}{2};

where

λ

is

MathematicsDefinite IntegrationJEE Main

Solution:

2324 Upvotes Verified Answer

The correct answer is: 3

max

(|\sin x|, |s i n^{- 1} (\sin x)|)

is

|\sin^{- 1} (\sin x)|

Hence,

I_{n} = n (\frac{1}{2} \cdot π \frac{π}{2})

=

\frac{n π^{2}}{4}

(area of triangle)

∴

I_{2} + I_{4} = \frac{6 π^{2}}{4}

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