integral from 0.5 to 1 of 3x^4+1/(2x)-5

解

\int_{0.5}^{1} 3 x^{4} + \frac{1}{2 x} - 5 d x

- 1.57217 \dots

解答ステップ

\int_{0.5}^{1} 3 x^{4} + \frac{1}{2 x} - 5 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_{0.5}^{1} 3 x^{4} d x + \int_{0.5}^{1} \frac{1}{2 x} d x - \int_{0.5}^{1} 5 d x

\int_{0.5}^{1} 3 x^{4} d x = 0.58125

\int_{0.5}^{1} \frac{1}{2 x} d x = 0.34657 \dots

\int_{0.5}^{1} 5 d x = 2.5

= 0.58125 + 0.34657 \dots - 2.5

簡素化

= - 1.57217 \dots