integral from 0 to 3y of (3+x^2+1/4 y^2)

解

\int_{0}^{3 y} (3 + x^{2} + \frac{1}{4} y^{2}) d x

9 y + 9 y^{3} + \frac{3 y ^{3}}{4}

解答ステップ

\int_{0}^{3 y} 3 + x^{2} + \frac{1}{4} y^{2} 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_{0}^{3 y} 3 d x + \int_{0}^{3 y} x^{2} d x + \int_{0}^{3 y} \frac{1}{4} y^{2} d x

\int_{0}^{3 y} 3 d x = 9 y

\int_{0}^{3 y} x^{2} d x = 9 y^{3}

\int_{0}^{3 y} \frac{1}{4} y^{2} d x = \frac{3 y ^{3}}{4}

= 9 y + 9 y^{3} + \frac{3 y ^{3}}{4}