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

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

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

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

\frac{125}{6}

Decimal

20.83333 \dots

Solution steps

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

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

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

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

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

Simplify

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

= \frac{125}{6}

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