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人気のある微分積分 >

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

解

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

解

2 (- ln (2 - 1) + 2)

+1

十進法表記

4.59117 \dots

解答ステップ

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

定数を除く:

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

= 4 \cdot \int_{- \frac{π}{4}}^{0} sec^{3} (x) d x

積分換算を適用する

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

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

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

簡素化

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

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

限度を計算する:

\frac{1}{2}

= 4 (\frac{1}{2} - \frac{1}{2} ln (2 - 1))

簡素化

= 2 (- ln (2 - 1) + 2)

グラフ

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