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人気のある微分積分 >

integral from 0 to 1 of sqrt(x^2-x^4)

解

\int_{0}^{1} x^{2} - x^{4} d x

解

\frac{1}{3}

+1

十進法表記

0.33333 \dots

解答ステップ

\int_{0}^{1} x^{2} - x^{4} d x

簡素化

x^{2} - x^{4} : x 1 - x^{2}

= \int_{0}^{1} x 1 - x^{2} d x

u置換積分法を適用する

= \int_{1}^{0} - u^{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} - u^{2} d u

定数を除く:

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

= - (- \int_{0}^{1} u^{2} d u)

べき乗則を適用する

= - (- [\frac{u ^{3}}{3}]_{0}^{1})

簡素化

= [\frac{u ^{3}}{3}]_{0}^{1}

限度を計算する:

\frac{1}{3}

= \frac{1}{3}

グラフ

人気の例

integral from 0 to 4 of sqrt(x)e^x

\int_{0}^{4} x e^{x} d x

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

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

integral from 4.6 to 7 of (12x^2-6x+4/x)

\int_{4.6}^{7} (12 x^{2} - 6 x + \frac{4}{x}) d x

integral from 0 to 1 of e^{e^x}

\int_{0}^{1} e^{e^{x}} d x

integral from 0 to 1 of 8t

\int_{0}^{1} 8 t d t