What is the integral from-2 to 2 of (19-|x|^3) ?

The integral from-2 to 2 of (19-|x|^3) is 68

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integral from-2 to 2 of (19-|x|^3)

\int_{- 2}^{2} (19 - ∣ x ∣^{3}) d x

68

Solution steps

\int_{- 2}^{2} 19 - ∣ x ∣^{3} d x

Eliminate Absolutes

= \int_{- 2}^{0} 19 - (- x)^{3} d x + \int_{0}^{2} 19 - x^{3} d x

\int_{- 2}^{0} 19 - (- x)^{3} d x = 34

\int_{0}^{2} 19 - x^{3} d x = 34

= 34 + 34

Simplify

= 68

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\int_{- 2}^{2} 4 - x^{2} + x^{3} d x

\int_{1}^{4} (x - 4)^{2} d x

What is the integral from-2 to 2 of (19-|x|^3) ?
The integral from-2 to 2 of (19-|x|^3) is 68