integral from 0 to 1 of 7tcosh(t)

解

\int_{0}^{1} 7 t cosh (t) d t

7 (- \frac{1}{e} + 1)

十進法表記

4.42484 \dots

解答ステップ

\int_{0}^{1} 7 t cosh (t) d t

定数を除く:

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

= 7 \cdot \int_{0}^{1} t cosh (t) d t

部分積分を適用する

= 7 [t sinh (t) - \int sinh (t) d t]_{0}^{1}

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

= 7 [t sinh (t) - cosh (t)]_{0}^{1}

限度を計算する:

- \frac{1}{e} + 1

= 7 (- \frac{1}{e} + 1)