What is the integral from-a to a of (a-|x|) ?

The integral from-a to a of (a-|x|) is 2a^2-a|a|

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

\int_{- a}^{a} (a - ∣ x ∣) d x

2 a^{2} - a ∣ a ∣

Solution steps

\int_{- a}^{a} a - ∣ x ∣ d x

Apply the Sum Rule:

\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 ∣

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

\frac{x + 7}{x + 1}

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

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

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

What is the integral from-a to a of (a-|x|) ?
The integral from-a to a of (a-|x|) is 2a^2-a|a|