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

The integral from-3 to 3 of |x|-(x^2-6) is 27

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integral from-3 to 3 of |x|-(x^2-6)

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x

27

Solution steps

\int_{- 3}^{3} ∣ x ∣ - (x^{2} - 6) d x

Eliminate Absolutes

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

\int_{- 3}^{0} - x - (x^{2} - 6) d x = \frac{27}{2}

\int_{0}^{3} x - (x^{2} - 6) d x = \frac{27}{2}

= \frac{27}{2} + \frac{27}{2}

Simplify

\frac{27}{2} + \frac{27}{2} : 27

= 27

What is the integral from-3 to 3 of |x|-(x^2-6) ?
The integral from-3 to 3 of |x|-(x^2-6) is 27