What is the integral from-4 to-2 of (-x+|-3x-9|) ?

The integral from-4 to-2 of (-x+|-3x-9|) is 9

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integral from-4 to-2 of (-x+|-3x-9|)

\int_{- 4}^{- 2} (- x + ∣ - 3 x - 9 ∣) d x

9

Solution steps

\int_{- 4}^{- 2} - x + ∣ - 3 x - 9 ∣ d x

Eliminate Absolutes

= \int_{- 4}^{- 3} - x - 3 x - 9 d x + \int_{- 3}^{- 2} - x + 3 x + 9 d x

\int_{- 4}^{- 3} - x - 3 x - 9 d x = 5

\int_{- 3}^{- 2} - x + 3 x + 9 d x = 4

= 5 + 4

Simplify

= 9

\frac{d y}{d x} = 2 y - y^{2}

\frac{d}{d x} (2 x^{7} - 3 x^{6} + 3 x^{3} - 4 x^{2} - 7)

\int \frac{7 - 7 x}{1 - x} d x

\int \frac{7}{3 - 3 x ^{2}} d x

\int x (x^{2} - 1)^{3} d x

What is the integral from-4 to-2 of (-x+|-3x-9|) ?
The integral from-4 to-2 of (-x+|-3x-9|) is 9