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

- \frac{1}{2} \cdot \frac{1}{( x ^{2} + 1 ) ^{2}}

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

\int_{5}^{6} \frac{x}{x - 5} d x

\int \frac{x ^{2}}{x + 5} d x

x = 9 y^{3}, x = 9 y^{2}

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