Let I = ∫ 0 1 sin ⁡ x x d x a n d J = ∫ 0 1 cos ⁡ x x d x . Then, which one of the following is true?

Question

Let I = ∫ 0 1 sin ⁡ x x d x a n d J = ∫ 0 1 cos ⁡ x x d x . Then, which one of the following is true?, I > 2 3 a n d J 2, I > 2 3 a n d J > 2, I 2 3 a n d J 2, I 2 3 a n d J > 2

MARKS App · Accepted Answer

Since, I = ∫ 0 1 sin ⁡ x x d x ∫ 0 1 x x d x as in x ∈ 0,1 , x > sin ⁡ x I ∫ 0 1 x d x = 2 3 x 3 / 2 0 1 ⇒ I 2 3 For, x ∈ 0,1 , cos ⁡ x x 1 x Hence, J = ∫ 0 1 cos ⁡ x x d x ∫ 0 1 x - 1 2 d x = 2 ⇒ J 2

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