integral from-1 to 1/2 of 4x^2-x+1/2

解

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

\frac{21}{8}

十進法表記

2.625

解答ステップ

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

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

\int_{- 1}^{\frac{1}{2}} x d x = - \frac{3}{8}

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

= \frac{3}{2} - (- \frac{3}{8}) + \frac{3}{4}

簡素化

\frac{3}{2} - (- \frac{3}{8}) + \frac{3}{4} : \frac{21}{8}

= \frac{21}{8}