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人気のある微分積分 >

integral from 0 to pi/4 of 2sec^3(x)

解

\int_{0}^{\frac{π}{4}} 2 sec^{3} (x) d x

解

2 + ln (1 + 2)

+1

十進法表記

2.29558 \dots

解答ステップ

\int_{0}^{\frac{π}{4}} 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}{4}} 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}{4}} + \frac{1}{2} \cdot \int_{0}^{\frac{π}{4}} sec (x) d x)

\int_{0}^{\frac{π}{4}} sec (x) d x = ln (1 + 2)

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

簡素化

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

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

限度を計算する:

\frac{1}{2}

= 2 \cdot \frac{1}{2} + ln (1 + 2)

簡素化

= 2 + ln (1 + 2)

グラフ

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