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人気のある微分積分 >

integral from 0 to a of (a-x)

解

\int_{0}^{a} (a - x) d x

解

a^{2} - \frac{a ^{2}}{2}

解答ステップ

\int_{0}^{a} a - x 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}^{a} a d x - \int_{0}^{a} x d x

\int_{0}^{a} a d x = a^{2}

\int_{0}^{a} x d x = \frac{a ^{2}}{2}

= a^{2} - \frac{a ^{2}}{2}

人気の例

integral from x to y of (2t+1)

\int_{x}^{y} (2 t + 1) d t

integral from-5 to 1 of 1/(10+2x)

\int_{- 5}^{1} \frac{1}{10 + 2 x} d x

integral from-7 to 2 of-x^2-3x

\int_{- 7}^{2} - x^{2} - 3 x d x

integral from 1 to 4 of (-x^2+5x-4)

\int_{1}^{4} (- x^{2} + 5 x - 4) d x

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

\int_{1}^{2} \frac{x ^{2} + 1}{x ^{3}} d x