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res2bfitjq

res2bfitjq

Answered question

2022-05-27

How to integrate 0 π / 2 sin ( x ) sin ( x + π 4 ) d x using substitution x = π 2 y ?

Answer & Explanation

pralkammj

pralkammj

Beginner2022-05-28Added 7 answers

Step 1
Let
I := 0 π / 2 sin x d x sin ( x + π / 4 ) = 0 π / 2 2 sin x d x sin x + cos x = 0 π / 2 2 cos y d y sin y + cos y
so, averaging the last two expressions,
I = 1 2 0 π / 2 d x = π 8 . .

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