integral from 0 to 4 of cos(sqrt(x)-1)

解

\int_{0}^{4} cos (x - 1) d x

2 cos (1) (2 sin (2) + cos (2) - 1) + 2 sin (1) (sin (2) - 2 cos (2))

十進法表記

3.36588 \dots

解答ステップ

\int_{0}^{4} cos (x - 1) d x

三角関数の公式を使用して書き換える

= \int_{0}^{4} cos (x) cos (1) + sin (x) sin (1) 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}^{4} cos (x) cos (1) d x + \int_{0}^{4} sin (x) sin (1) d x

\int_{0}^{4} cos (x) cos (1) d x = 2 cos (1) (2 sin (2) + cos (2) - 1)

\int_{0}^{4} sin (x) sin (1) d x = 2 sin (1) (sin (2) - 2 cos (2))

= 2 cos (1) (2 sin (2) + cos (2) - 1) + 2 sin (1) (sin (2) - 2 cos (2))