What is the integral from-1 to 4 of |x-3x^2| ?

The integral from-1 to 4 of |x-3x^2| is 3107/54

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integral from-1 to 4 of |x-3x^2|

\int_{- 1}^{4} x - 3 x^{2} d x

\frac{3107}{54}

Decimal Notation

57.53703 \dots

Solution steps

\int_{- 1}^{4} x - 3 x^{2} d x

Eliminate Absolutes

= \int_{- 1}^{0} - x + 3 x^{2} d x + \int_{0}^{\frac{1}{3}} x - 3 x^{2} d x + \int_{\frac{1}{3}}^{4} - x + 3 x^{2} d x

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

\int_{0}^{\frac{1}{3}} x - 3 x^{2} d x = \frac{1}{54}

\int_{\frac{1}{3}}^{4} - x + 3 x^{2} d x = \frac{3025}{54}

= \frac{3}{2} + \frac{1}{54} + \frac{3025}{54}

Simplify

\frac{3}{2} + \frac{1}{54} + \frac{3025}{54} : \frac{3107}{54}

= \frac{3107}{54}

(x e^{x^{2}})^{^{'}}

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

\frac{d}{d x} (x + 1 - 1)

e^{3 x c o s (2 x)}

y = - \frac{3}{x} + \frac{2}{x ^{3}}

What is the integral from-1 to 4 of |x-3x^2| ?
The integral from-1 to 4 of |x-3x^2| is 3107/54