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人気のある微分積分 >

integral from 0 to 1 of (e^x-e^{-x})/2

解

\int_{0}^{1} \frac{e ^{x} - e ^{- x}}{2} d x

解

\frac{e ^{2} + 1}{2 e} - 1

+1

十進法表記

0.54308 \dots

解答ステップ

\int_{0}^{1} \frac{e ^{x} - e ^{- x}}{2} d x

定数を除く:

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

= \frac{1}{2} \cdot \int_{0}^{1} e^{x} - e^{- x} d x

三角関数の公式を使用して書き換える

= \frac{1}{2} \cdot \int_{0}^{1} 2 sinh (x) d x

定数を除く:

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

= \frac{1}{2} \cdot 2 \cdot \int_{0}^{1} sinh (x) d x

共通積分を使用する:

\int sinh (x) d x = cosh (x)

= \frac{1}{2} \cdot 2 [cosh (x)]_{0}^{1}

簡素化

\frac{1}{2} \cdot 2 [cosh (x)]_{0}^{1} : [cosh (x)]_{0}^{1}

= [cosh (x)]_{0}^{1}

限度を計算する:

\frac{e ^{2} + 1}{2 e} - 1

= \frac{e ^{2} + 1}{2 e} - 1

グラフ

人気の例

integral from 0 to ln(2) of e^{x+y}

\int_{0}^{l n (2)} e^{x + y} d y

integral from 1 to 3 of (2ln(x))/x

\int_{1}^{3} \frac{2 ln ( x )}{x} d x

integral from 0 to 1 of sin(x)cos(x)

\int_{0}^{1} sin (x) cos (x) d x

integral from 1 to 1 of sqrt(1+x^4)

\int_{1}^{1} 1 + x^{4} d x

integral from 1 to 3 of 2(1+ln(x))x^{2x}

\int_{1}^{3} 2 (1 + ln (x)) x^{2 x} d x