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人気のある微分積分 >

integral from 0 to pi/6 of 2sec^3(x)

解

\int_{0}^{\frac{π}{6}} 2 sec^{3} (x) d x

解

2 (\frac{1}{3} + \frac{1}{4} ln (3))

+1

十進法表記

1.21597 \dots

解答ステップ

\int_{0}^{\frac{π}{6}} 2 sec^{3} (x) d x

定数を除く:

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

= 2 \cdot \int_{0}^{\frac{π}{6}} sec^{3} (x) d x

積分換算を適用する

= 2 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{6}} + \frac{1}{2} \cdot \int_{0}^{\frac{π}{6}} sec (x) d x)

\int_{0}^{\frac{π}{6}} sec (x) d x = \frac{1}{2} ln (3)

= 2 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{6}} + \frac{1}{2} \cdot \frac{1}{2} ln (3))

簡素化

2 ([\frac{sec ^{2} ( x ) sin ( x )}{2}]_{0}^{\frac{π}{6}} + \frac{1}{2} \cdot \frac{1}{2} ln (3)) : 2 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{6}} + \frac{1}{4} ln (3))

= 2 ([\frac{1}{2} sec (x) tan (x)]_{0}^{\frac{π}{6}} + \frac{1}{4} ln (3))

限度を計算する:

\frac{1}{3}

= 2 (\frac{1}{3} + \frac{1}{4} ln (3))

グラフ

人気の例

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\int 1 - e^{- x} d x

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\int_{1}^{7} \frac{x + 1}{x ^{2} + 2 x - 1} d x

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d er i v a t i v e y = \frac{π ^{2} x ^{6} + 9000}{x ^{2}}

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