What is the integral from-2 to 1 of (x^2-6x+12) ?

The integral from-2 to 1 of (x^2-6x+12) is 48

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integral from-2 to 1 of (x^2-6x+12)

\int_{- 2}^{1} (x^{2} - 6 x + 12) d x

48

Solution steps

\int_{- 2}^{1} x^{2} - 6 x + 12 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

= \int_{- 2}^{1} x^{2} d x - \int_{- 2}^{1} 6 x d x + \int_{- 2}^{1} 12 d x

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

\int_{- 2}^{1} 6 x d x = - 9

\int_{- 2}^{1} 12 d x = 36

= 3 - (- 9) + 36

Simplify

= 48

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

\int (sec^{2} (x) + 7) d x

f (x) = - 3 x^{4}, at x = - 1

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

x \to \infty lim (8^{- x})

What is the integral from-2 to 1 of (x^2-6x+12) ?
The integral from-2 to 1 of (x^2-6x+12) is 48