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人気のある微分積分 >

integral from 0 to pi/6 of 3sec(θ)tan(θ)

解

\int_{0}^{\frac{π}{6}} 3 sec (θ) tan (θ) d θ

解

3 (\frac{2}{3} - 1)

+1

十進法表記

0.46410 \dots

解答ステップ

\int_{0}^{\frac{π}{6}} 3 sec (θ) tan (θ) d θ

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{0}^{\frac{π}{6}} sec (θ) tan (θ) d θ

u置換積分法を適用する

= 3 \cdot \int_{1}^{\frac{2 3}{3}} 1 d u

定数の積分:

\int a d x = a x

= 3 [1 \cdot u]_{1}^{\frac{2 3}{3}}

簡素化

3 [1 \cdot u]_{1}^{\frac{2 3}{3}} : 3 [u]_{1}^{\frac{2}{3}}

= 3 [u]_{1}^{\frac{2}{3}}

限度を計算する:

\frac{2}{3} - 1

= 3 (\frac{2}{3} - 1)

グラフ

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