integral from 0 to 2 of 1+cos(x^2)

解

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

2 + \frac{π}{2} C (\frac{2}{π} \cdot 2) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

解答ステップ

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

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

\int_{0}^{2} cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} \cdot 2) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= 2 + \frac{π}{2} C (\frac{2}{π} \cdot 2) - \frac{π}{2} C (\frac{2}{π} \cdot 0)