What is the integral from-1 to 4 of |x-2x^2| ?

The integral from-1 to 4 of |x-2x^2| is 431/12

integral from-1 to 4 of |x-2x^2|

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

\frac{431}{12}

Decimal

35.91666 \dots

Solution steps

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

Eliminate Absolutes

= \int_{- 1}^{0} - x + 2 x^{2} d x + \int_{0}^{\frac{1}{2}} x - 2 x^{2} d x + \int_{\frac{1}{2}}^{4} - x + 2 x^{2} d x

\int_{- 1}^{0} - x + 2 x^{2} d x = \frac{7}{6}

\int_{0}^{\frac{1}{2}} x - 2 x^{2} d x = \frac{1}{24}

\int_{\frac{1}{2}}^{4} - x + 2 x^{2} d x = \frac{833}{24}

= \frac{7}{6} + \frac{1}{24} + \frac{833}{24}

Simplify

\frac{7}{6} + \frac{1}{24} + \frac{833}{24} : \frac{431}{12}

= \frac{431}{12}

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What is the integral from-1 to 4 of |x-2x^2| ?
The integral from-1 to 4 of |x-2x^2| is 431/12