integral from 0 to y of 2(x+y)

解

\int_{0}^{y} 2 (x + y) d x

3 y^{2}

解答ステップ

\int_{0}^{y} 2 (x + y) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{y} y + x 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

= 2 (\int_{0}^{y} y d x + \int_{0}^{y} x d x)

\int_{0}^{y} y d x = y^{2}

\int_{0}^{y} x d x = \frac{y ^{2}}{2}

= 2 (y^{2} + \frac{y ^{2}}{2})

簡素化

2 (y^{2} + \frac{y ^{2}}{2}) : 3 y^{2}

= 3 y^{2}