What is the integral from-8 to 8 of |7x|-(x^2-8) ?

The integral from-8 to 8 of |7x|-(x^2-8) is 704/3

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integral from-8 to 8 of |7x|-(x^2-8)

\int_{- 8}^{8} ∣ 7 x ∣ - (x^{2} - 8) d x

\frac{704}{3}

Decimal

234.66666 \dots

Solution steps

\int_{- 8}^{8} ∣ 7 x ∣ - (x^{2} - 8) d x

Eliminate Absolutes

= \int_{- 8}^{0} - 7 x - (x^{2} - 8) d x + \int_{0}^{8} 7 x - (x^{2} - 8) d x

\int_{- 8}^{0} - 7 x - (x^{2} - 8) d x = \frac{352}{3}

\int_{0}^{8} 7 x - (x^{2} - 8) d x = \frac{352}{3}

= \frac{352}{3} + \frac{352}{3}

Simplify

\frac{352}{3} + \frac{352}{3} : \frac{704}{3}

= \frac{704}{3}

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What is the integral from-8 to 8 of |7x|-(x^2-8) ?
The integral from-8 to 8 of |7x|-(x^2-8) is 704/3