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

解

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

\frac{y ^{4} - y ^{2}}{2} + 2 y^{3} - 2 y^{2}

解答ステップ

\int_{y}^{y^{2}} x + 2 y 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_{y}^{y^{2}} x d x + \int_{y}^{y^{2}} 2 y d x

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

\int_{y}^{y^{2}} 2 y d x = 2 y^{3} - 2 y^{2}

= \frac{y ^{4} - y ^{2}}{2} + 2 y^{3} - 2 y^{2}