What is the integral from-1 to 3 of |6x^2-x^3-8x| ?

The integral from-1 to 3 of |6x^2-x^3-8x| is 12

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integral from-1 to 3 of |6x^2-x^3-8x|

\int_{- 1}^{3} 6 x^{2} - x^{3} - 8 x d x

12

Solution steps

\int_{- 1}^{3} 6 x^{2} - x^{3} - 8 x d x

Eliminate Absolutes

= \int_{- 1}^{0} 6 x^{2} - x^{3} - 8 x d x + \int_{0}^{2} - 6 x^{2} + x^{3} + 8 x d x + \int_{2}^{3} 6 x^{2} - x^{3} - 8 x d x

\int_{- 1}^{0} 6 x^{2} - x^{3} - 8 x d x = \frac{25}{4}

\int_{0}^{2} - 6 x^{2} + x^{3} + 8 x d x = 4

\int_{2}^{3} 6 x^{2} - x^{3} - 8 x d x = \frac{7}{4}

= \frac{25}{4} + 4 + \frac{7}{4}

Simplify

\frac{25}{4} + 4 + \frac{7}{4} : 12

= 12

\int_{0}^{1} \frac{x}{1 - x} d x

\int_{0}^{2} x^{3} - 4 x + 3 d x

\int_{2}^{3} \frac{2}{x ^{3}} d x

\int_{0}^{x} \frac{1}{1 - t} d t

\int_{0}^{4} (4 x - 3 x) d x

What is the integral from-1 to 3 of |6x^2-x^3-8x| ?
The integral from-1 to 3 of |6x^2-x^3-8x| is 12