I need to solve \int^{\frac{\pi}{2}}_0 \cos^6 xdx I tried to

Naima Cox

Naima Cox

Answered question

2022-01-22

I need to solve 0π2cos6xdx I tried to use cos(3x)=4cos3x3cosx but not succeeded

Answer & Explanation

Georgia Ingram

Georgia Ingram

Beginner2022-01-23Added 11 answers

Hint: Use that
cos6x=132(15cos(2x)+6cos(4x)+cos(6x)+10)
Ydaxq

Ydaxq

Beginner2022-01-24Added 12 answers

2I=0π2(cos6x+sin6x)dx
Now c6+s6=(c2+s2)33c2s2(c2+s2)=13(2cs)24
8I=0π2(43sin22x)dx
16I=0π2(83(1cos4x))dx=?

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