What is the integral from 2 to-1 of 3x(x-4) ?

The integral from 2 to-1 of 3x(x-4) is 9

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integral from 2 to-1 of 3x(x-4)

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

9

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int_{- 1}^{2} x (x - 4) d x

Expand

x (x - 4) : x^{2} - 4 x

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int_{- 1}^{2} 4 x d x = 6

= - 3 (3 - 6)

Simplify

= 9

\int_{0}^{1} \frac{1}{x + 1} d x

\int x x - 1 d x

x^{2} - 5

x \to 5 lim (500)

x \to 3 + lim (ln (x))

What is the integral from 2 to-1 of 3x(x-4) ?
The integral from 2 to-1 of 3x(x-4) is 9