integral from 3 to 0 of 15w^4-13w^2+w

解

\int_{3}^{0} 15 w^{4} - 13 w^{2} + w d w

- \frac{1233}{2}

十進法表記

- 616.5

解答ステップ

\int_{3}^{0} 15 w^{4} - 13 w^{2} + w d w

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{3} 15 w^{4} - 13 w^{2} + w d w

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}^{3} 15 w^{4} d w - \int_{0}^{3} 13 w^{2} d w + \int_{0}^{3} w d w)

\int_{0}^{3} 15 w^{4} d w = 729

\int_{0}^{3} 13 w^{2} d w = 117

\int_{0}^{3} w d w = \frac{9}{2}

= - (729 - 117 + \frac{9}{2})

簡素化

- (729 - 117 + \frac{9}{2}) : - \frac{1233}{2}

= - \frac{1233}{2}