integral from 0 to 1 of 5-(-3/2 x+4)

解

\int_{0}^{1} 5 - (- \frac{3}{2} x + 4) d x

\frac{7}{4}

十進法表記

1.75

解答ステップ

\int_{0}^{1} 5 - (- \frac{3}{2} x + 4) d x

簡素化

= \int_{0}^{1} \frac{3}{2} x + 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}^{1} \frac{3}{2} x d x + \int_{0}^{1} 1 d x

\int_{0}^{1} \frac{3}{2} x d x = \frac{3}{4}

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

= \frac{3}{4} + 1

簡素化

\frac{3}{4} + 1 : \frac{7}{4}

= \frac{7}{4}