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

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

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

\frac{431}{12}

Decimal Notation

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}

\frac{\partial}{\partial x} (x y e^{y})

f (x) = 2^{s i n (x)}

y = (\frac{8}{x})^{5 x}

\frac{d}{d x} (ln (x + x^{2} + 5))

\int_{1}^{3} \frac{1}{x ^{2} - 2 x + 5} d x

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