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人気のある微分積分 >

integral from-a to a of (a-|x|)

解

\int_{- a}^{a} (a - ∣ x ∣) d x

解

2 a^{2} - a ∣ a ∣

解答ステップ

\int_{- a}^{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_{- a}^{a} a d x - \int_{- a}^{a} ∣ x ∣ d x

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

\int_{- a}^{a} ∣ x ∣ d x = a ∣ a ∣

= 2 a^{2} - a ∣ a ∣

人気の例

limit as a approaches 0 of x^a

a \to 0 lim (x^{a})

tangent (x+7)/(x+1)

t an g e n t \frac{x + 7}{x + 1}

tangent y=4x^3-4x,(1,0)

t an g e n t y = 4 x^{3} - 4 x, (1, 0)

integral of (x+5)(x^3+5x-10)

\int (x + 5) (x^{3} + 5 x - 10) d x

integral of-x^2ln(x)

\int - x^{2} ln (x) d x