integral from 1 to a of (1/(sqrt(4x)))

解

\int_{1}^{a} (\frac{1}{4 x}) d x

a - 1

解答ステップ

\int_{1}^{a} \frac{1}{4 x} d x

部分積分を適用する

= [\frac{1}{2} x - \int - \frac{1}{4 x ^{\frac{1}{2}}} d x]_{1}^{a}

\int - \frac{1}{4 x ^{\frac{1}{2}}} d x = - \frac{1}{2} x^{\frac{1}{2}}

= [\frac{1}{2} x - (- \frac{1}{2} x^{\frac{1}{2}})]_{1}^{a}

簡素化

[\frac{1}{2} x - (- \frac{1}{2} x^{\frac{1}{2}})]_{1}^{a} : [\frac{1}{2} (x + x)]_{1}^{a}

= [\frac{1}{2} (x + x)]_{1}^{a}

限度を計算する:

a - 1

= a - 1