integral from 0 to 1 of (x+6sqrt(1-x^2))

解

\int_{0}^{1} (x + 6 1 - x^{2}) d x

\frac{1}{2} + \frac{3 π}{2}

十進法表記

5.21238 \dots

解答ステップ

\int_{0}^{1} x + 6 1 - x^{2} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x d x + \int_{0}^{1} 6 1 - x^{2} d x

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

\int_{0}^{1} 6 1 - x^{2} d x = \frac{3 π}{2}

= \frac{1}{2} + \frac{3 π}{2}