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人気のある微分積分 >

integral from 0 to 2 of xy^2

解

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

解

y^{2} \cdot 2

解答ステップ

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

定数を除く:

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

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

べき乗則を適用する

= y^{2} [\frac{x ^{2}}{2}]_{0}^{2}

限度を計算する:

2

= y^{2} \cdot 2

人気の例

integral from 0 to 2 of x 3/4 x(2-x)

\int_{0}^{2} x \frac{3}{4} x (2 - x) d x

integral from 0 to infinity of x/(x^2+9)

\int_{0}^{\infty} \frac{x}{x ^{2} + 9} d x

integral from 2 to x of x

\int_{2}^{x} x d x

integral from 0 to t of (u^2-u+e^u)

\int_{0}^{t} (u^{2} - u + e^{u}) d u

integral from 0 to 1-x of y

\int_{0}^{1 - x} y d y