What is the integral from-2 to 2 of (6-x^2)-|x| ?

The integral from-2 to 2 of (6-x^2)-|x| is 44/3

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integral from-2 to 2 of (6-x^2)-|x|

\int_{- 2}^{2} (6 - x^{2}) - ∣ x ∣ d x

\frac{44}{3}

Decimal

14.66666 \dots

Solution steps

\int_{- 2}^{2} 6 - x^{2} - ∣ x ∣ d x

Eliminate Absolutes

= \int_{- 2}^{0} 6 - x^{2} - (- x) d x + \int_{0}^{2} 6 - x^{2} - x d x

\int_{- 2}^{0} 6 - x^{2} - (- x) d x = \frac{22}{3}

\int_{0}^{2} 6 - x^{2} - x d x = \frac{22}{3}

= \frac{22}{3} + \frac{22}{3}

Simplify

\frac{22}{3} + \frac{22}{3} : \frac{44}{3}

= \frac{44}{3}

\int_{- π}^{π} ∣ sin (t) ∣ d t

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

\int_{0}^{x} \frac{3 + t ^{2}}{1 - t ^{4}} d t

\int_{1}^{2} \frac{x ^{2} - a}{x} d x

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

What is the integral from-2 to 2 of (6-x^2)-|x| ?
The integral from-2 to 2 of (6-x^2)-|x| is 44/3