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

The integral from-2 to 2 of |2x^2-2x| is 34/3

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

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

\frac{34}{3}

Decimal Notation

11.33333 \dots

Solution steps

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

Eliminate Absolutes

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

\int_{- 2}^{0} 2 x^{2} - 2 x d x = \frac{28}{3}

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

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

= \frac{28}{3} + \frac{1}{3} + \frac{5}{3}

Simplify

\frac{28}{3} + \frac{1}{3} + \frac{5}{3} : \frac{34}{3}

= \frac{34}{3}

\int_{0}^{x} f (t) d t

f (x) = \frac{3}{1 + x ^{2}}

\frac{\partial}{\partial x} (- \frac{2 y}{( 2 x + 3 y ) ^{2}})

y^{^{'}} = 2 y, y (0) = 1

\frac{d}{d x} (3 x^{2} x)

What is the integral from-2 to 2 of |2x^2-2x| ?
The integral from-2 to 2 of |2x^2-2x| is 34/3