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人気のある微分積分 >

integral from 0 to 20 of 2^{t/(10)}

解

\int_{0}^{20} 2^{\frac{t}{10}} d t

解

\frac{30}{ln ( 2 )}

+1

十進法表記

43.28085 \dots

解答ステップ

\int_{0}^{20} 2^{\frac{t}{10}} d t

u置換積分法を適用する

= \int_{0}^{2} 5 \cdot 2^{u + 1} d u

定数を除く:

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

= 5 \cdot \int_{0}^{2} 2^{u + 1} d u

2^{u + 1} = 2^{1} \cdot 2^{u}

= 5 \cdot \int_{0}^{2} 2^{1} \cdot 2^{u} d u

定数を除く:

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

= 5 \cdot 2^{1} \cdot \int_{0}^{2} 2^{u} d u

簡素化

= 5 \cdot 2 \cdot \int_{0}^{2} 2^{u} d u

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

= 5 \cdot 2 [\frac{2 ^{u}}{ln ( 2 )}]_{0}^{2}

簡素化

= 10 [\frac{2 ^{u}}{ln ( 2 )}]_{0}^{2}

限度を計算する:

\frac{3}{ln ( 2 )}

= 10 \cdot \frac{3}{ln ( 2 )}

簡素化

= \frac{30}{ln ( 2 )}

グラフ

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