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shmilybaby4i

shmilybaby4i

Answered question

2022-06-12

Prove 0 1 / 2 cos π x x 2 + 1 1 4 tan 1 1 2

Answer & Explanation

kuncwadi17

kuncwadi17

Beginner2022-06-13Added 16 answers

I assume that there is a square missing in the left hand side, since the inequality as stated is false. Then by Cauchy–Schwarz inequality:
( 0 1 2 cos ( π x ) x 2 + 1 d x ) 2 0 1 2 cos 2 ( π x ) d x 0 1 2 1 x 2 + 1 d x = 1 4 arctan ( 1 2 )

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