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

The integral from-2 to-1 of (2x^2)-(2x+6) is 5/3

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

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

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

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

Simplify

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

\int_{- 2}^{- 1} 2 x^{2} d x = \frac{14}{3}

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

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

= \frac{14}{3} - (- 3) - 6

Simplify

\frac{14}{3} - (- 3) - 6 : \frac{5}{3}

= \frac{5}{3}

What is the integral from-2 to-1 of (2x^2)-(2x+6) ?
The integral from-2 to-1 of (2x^2)-(2x+6) is 5/3