integral from 0 to pi/2 of 10+sin(x)-x^2

解

\int_{0}^{\frac{π}{2}} 10 + sin (x) - x^{2} d x

5 π + 1 - \frac{π ^{3}}{24}

十進法表記

15.41603 \dots

解答ステップ

\int_{0}^{\frac{π}{2}} 10 + sin (x) - 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}^{\frac{π}{2}} 10 d x + \int_{0}^{\frac{π}{2}} sin (x) d x - \int_{0}^{\frac{π}{2}} x^{2} d x

\int_{0}^{\frac{π}{2}} 10 d x = 5 π

\int_{0}^{\frac{π}{2}} sin (x) d x = 1

\int_{0}^{\frac{π}{2}} x^{2} d x = \frac{π ^{3}}{24}

= 5 π + 1 - \frac{π ^{3}}{24}