What is the integral from-7 to 7 of |6x|-(x^2-7) ?

The integral from-7 to 7 of |6x|-(x^2-7) is 490/3

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integral from-7 to 7 of |6x|-(x^2-7)

\int_{- 7}^{7} ∣ 6 x ∣ - (x^{2} - 7) d x

\frac{490}{3}

Decimal

163.33333 \dots

Solution steps

\int_{- 7}^{7} ∣ 6 x ∣ - (x^{2} - 7) d x

Eliminate Absolutes

= \int_{- 7}^{0} - 6 x - (x^{2} - 7) d x + \int_{0}^{7} 6 x - (x^{2} - 7) d x

\int_{- 7}^{0} - 6 x - (x^{2} - 7) d x = \frac{245}{3}

\int_{0}^{7} 6 x - (x^{2} - 7) d x = \frac{245}{3}

= \frac{245}{3} + \frac{245}{3}

Simplify

\frac{245}{3} + \frac{245}{3} : \frac{490}{3}

= \frac{490}{3}

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What is the integral from-7 to 7 of |6x|-(x^2-7) ?
The integral from-7 to 7 of |6x|-(x^2-7) is 490/3