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

The integral from-2 to 2 of-3|x^2-4x| is -48

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

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

- 48

Solution steps

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

Eliminate Absolutes

= \int_{- 2}^{0} - 3 (x^{2} - 4 x) d x + \int_{0}^{2} - 3 (- x^{2} + 4 x) d x

\int_{- 2}^{0} - 3 (x^{2} - 4 x) d x = - 32

\int_{0}^{2} - 3 (- x^{2} + 4 x) d x = - 16

= - 32 - 16

Simplify

= - 48

\int \frac{5}{x ^{2} + 3 x - 4} d x

\int (5 x - 3)^{4} d x

y = \frac{x ^{2}}{3} + x + \frac{1}{2}

\frac{90}{x}

\int_{0}^{2} \frac{x}{( 1 + x ^{2} ) ^{2}} d x

What is the integral from-2 to 2 of-3|x^2-4x| ?
The integral from-2 to 2 of-3|x^2-4x| is -48