integral from 20 to 30 of k(x^2+y^2)

解

\int_{20}^{30} k (x^{2} + y^{2}) d y

k (10 x^{2} + \frac{19000}{3})

解答ステップ

\int_{20}^{30} k (x^{2} + y^{2}) d y

定数を除く:

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

= k \cdot \int_{20}^{30} x^{2} + y^{2} d y

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

= k (\int_{20}^{30} x^{2} d y + \int_{20}^{30} y^{2} d y)

\int_{20}^{30} x^{2} d y = 10 x^{2}

\int_{20}^{30} y^{2} d y = \frac{19000}{3}

= k (10 x^{2} + \frac{19000}{3})