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人気のある微分積分 >

integral from pi/6 to pi/2 of xcsc^2(x)

解

\int_{\frac{π}{6}}^{\frac{π}{2}} x csc^{2} (x) d x

解

\frac{π}{2 3} + ln (2)

+1

十進法表記

1.60004 \dots

解答ステップ

\int_{\frac{π}{6}}^{\frac{π}{2}} x csc^{2} (x) d x

部分積分を適用する

= [- x cot (x) - \int - cot (x) d x]_{\frac{π}{6}}^{\frac{π}{2}}

\int - cot (x) d x = - ln ∣ sin (x) ∣

= [- x cot (x) - (- ln ∣ sin (x) ∣)]_{\frac{π}{6}}^{\frac{π}{2}}

簡素化

= [- x cot (x) + ln ∣ sin (x) ∣]_{\frac{π}{6}}^{\frac{π}{2}}

限度を計算する:

- (- \frac{π}{2 3} - ln (2))

= - (- \frac{π}{2 3} - ln (2))

簡素化

= \frac{π}{2 3} + ln (2)

グラフ

人気の例

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