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人気のある微分積分 >

integral from-h to h of (y^2-h^2)

解

\int_{- h}^{h} (y^{2} - h^{2}) d y

解

\frac{2 h ^{3}}{3} - 2 h^{3}

解答ステップ

\int_{- h}^{h} y^{2} - h^{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

= \int_{- h}^{h} y^{2} d y - \int_{- h}^{h} h^{2} d y

\int_{- h}^{h} y^{2} d y = \frac{2 h ^{3}}{3}

\int_{- h}^{h} h^{2} d y = 2 h^{3}

= \frac{2 h ^{3}}{3} - 2 h^{3}

人気の例

integral from 0 to 2 of rsqrt(16-r^2)

\int_{0}^{2} r 16 - r^{2} d r

integral from 1 to 4 of (3sqrt(x))

\int_{1}^{4} (3 x) d x

integral from 4 to 0 of (2x^5+3x^4-2x^3)

\int_{4}^{0} (2 x^{5} + 3 x^{4} - 2 x^{3}) d x

integral from-1 to 1 of (8x^3-6x+1)

\int_{- 1}^{1} (8 x^{3} - 6 x + 1) d x

integral from 1 to 3 of 1/(x^2-16)

\int_{1}^{3} \frac{1}{x ^{2} - 16} d x