pi-pi-x-2020-sin-x-cos-x-dx-8-find-pi-pi-x-2020-cos-x-dx-

Question Number 85097 by jagoll last updated on 19/Mar/20

\underset{- π}{\int^{π}} x^{2020} (\sin x + \cos x) dx = 8

find \underset{- π}{\int^{π}} x^{2020} \cos x dx = ?

Answered by john santu last updated on 19/Mar/20

\Rightarrow 8 = \underset{- π}{\int^{π}} x^{2020} \sin x dx + \underset{- π}{\int^{π}} x^{2020} \cos x dx

(1) \underset{- π}{\int^{π}} x^{2020} \sin x dx = 0

(2) \underset{- π}{\int^{π}} x^{2020} \cos x dx = 2 \underset{0}{\int^{π}} x^{2020} \cos x dx

\Rightarrow 8 = 0 + 2 \underset{0}{\int^{π}} x^{2020} \cos x dx

\Rightarrow \underset{0}{\int^{π}} x^{2020} \cos x dx = 4

Commented by jagoll last updated on 19/Mar/20

thank you mister

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