What is the integral from-2 to 3 of (x-6)-(x^2-12) ?

The integral from-2 to 3 of (x-6)-(x^2-12) is 125/6

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integral from-2 to 3 of (x-6)-(x^2-12)

\int_{- 2}^{3} (x - 6) - (x^{2} - 12) d x

\frac{125}{6}

Decimal

20.83333 \dots

Solution steps

\int_{- 2}^{3} x - 6 - (x^{2} - 12) d x

Simplify

= \int_{- 2}^{3} - x^{2} + x + 6 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}^{3} x^{2} d x + \int_{- 2}^{3} x d x + \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

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

\int_{- 2}^{3} 6 d x = 30

= - \frac{35}{3} + \frac{5}{2} + 30

Simplify

- \frac{35}{3} + \frac{5}{2} + 30 : \frac{125}{6}

= \frac{125}{6}

x \to 1 lim (\frac{8}{x ^{3} - 1})

x \to 0 lim (7 x)

\frac{d}{d x} (ln (\frac{x + a}{x - a}))

x \to 0 lim (\frac{∣ - 2 x ∣}{5 x})

\frac{\partial}{\partial x} (34)

What is the integral from-2 to 3 of (x-6)-(x^2-12) ?
The integral from-2 to 3 of (x-6)-(x^2-12) is 125/6