Let P(x)=x^4+x^2+1. Then int 1−1P(sin x)P′(sin x)dx=?

vagnhestagn

vagnhestagn

Answered question

2022-09-29

Let P ( x ) = x 4 + x 2 + 1. Then 1 1 P ( sin x ) P ( sin x ) d x = ? ?

Answer & Explanation

bewagox7

bewagox7

Beginner2022-09-30Added 10 answers

The polynomial P is even, so your integrand f ( x ) = P ( sin x ) P ( sin x ) is odd.
Hence, without any calculation:
1 1 f ( x ) d x = 0.

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