What is the integral from-4 to 3 of |x^3-7x+6| ?

The integral from-4 to 3 of |x^3-7x+6| is 203/4

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integral from-4 to 3 of |x^3-7x+6|

\int_{- 4}^{3} x^{3} - 7 x + 6 d x

\frac{203}{4}

Decimal Notation

50.75

Solution steps

\int_{- 4}^{3} x^{3} - 7 x + 6 d x

Eliminate Absolutes

= \int_{- 4}^{- 3} - x^{3} + 7 x - 6 d x + \int_{- 3}^{1} x^{3} - 7 x + 6 d x + \int_{1}^{2} - x^{3} + 7 x - 6 d x + \int_{2}^{3} x^{3} - 7 x + 6 d x

\int_{- 4}^{- 3} - x^{3} + 7 x - 6 d x = \frac{53}{4}

\int_{- 3}^{1} x^{3} - 7 x + 6 d x = 32

\int_{1}^{2} - x^{3} + 7 x - 6 d x = \frac{3}{4}

\int_{2}^{3} x^{3} - 7 x + 6 d x = \frac{19}{4}

= \frac{53}{4} + 32 + \frac{3}{4} + \frac{19}{4}

Simplify

\frac{53}{4} + 32 + \frac{3}{4} + \frac{19}{4} : \frac{203}{4}

= \frac{203}{4}

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What is the integral from-4 to 3 of |x^3-7x+6| ?
The integral from-4 to 3 of |x^3-7x+6| is 203/4