integral from 2 to 4 of x^2y+y^2x+x+y

解

\int_{2}^{4} x^{2} y + y^{2} x + x + y d x

2 y + 6 + y^{2} \cdot 6 + \frac{56 y}{3}

解答ステップ

\int_{2}^{4} x^{2} y + y^{2} x + x + 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_{2}^{4} y d x + \int_{2}^{4} x d x + \int_{2}^{4} y^{2} x d x + \int_{2}^{4} y x^{2} d x

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

\int_{2}^{4} x d x = 6

\int_{2}^{4} y^{2} x d x = y^{2} \cdot 6

\int_{2}^{4} y x^{2} d x = \frac{56 y}{3}

= 2 y + 6 + y^{2} \cdot 6 + \frac{56 y}{3}