integral from 0 to 1 of 4/(pi(1+x^2))

解

\int_{0}^{1} \frac{4}{π ( 1 + x ^{2} )} d x

1

解答ステップ

\int_{0}^{1} \frac{4}{π ( 1 + x ^{2} )} d x

定数を除く:

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

= \frac{4}{π} \cdot \int_{0}^{1} \frac{1}{1 + x ^{2}} d x

共通積分を使用する:

\int \frac{1}{1 + x ^{2}} d x = arctan (x)

= \frac{4}{π} [arctan (x)]_{0}^{1}

限度を計算する:

\frac{π}{4}

= \frac{4}{π} \cdot \frac{π}{4}

簡素化

= 1