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人気のある微分積分 >

integral from 1 to 2 of 12x^22^{x^3}

解

\int_{1}^{2} 12 x^{2} 2^{x^{3}} d x

解

\frac{1016}{ln ( 2 )}

+1

十進法表記

1465.77816 \dots

解答ステップ

\int_{1}^{2} 12 x^{2} \cdot 2^{x^{3}} d x

定数を除く:

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

= 12 \cdot \int_{1}^{2} x^{2} \cdot 2^{x^{3}} d x

u置換積分法を適用する

= 12 \cdot \int_{1}^{8} \frac{2 ^{u}}{3} d u

定数を除く:

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

= 12 \cdot \frac{1}{3} \cdot \int_{1}^{8} 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 12 \cdot \frac{1}{3} [\frac{2 ^{u}}{ln ( 2 )}]_{1}^{8}

簡素化

12 \cdot \frac{1}{3} [\frac{2 ^{u}}{ln ( 2 )}]_{1}^{8} : 4 [\frac{2 ^{u}}{ln ( 2 )}]_{1}^{8}

= 4 [\frac{2 ^{u}}{ln ( 2 )}]_{1}^{8}

限度を計算する:

\frac{254}{ln ( 2 )}

= 4 \cdot \frac{254}{ln ( 2 )}

簡素化

= \frac{1016}{ln ( 2 )}

グラフ

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