What is the integral from-3 to 2 of (9-x^2)-(x+3) ?

The integral from-3 to 2 of (9-x^2)-(x+3) is 125/6

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integral from-3 to 2 of (9-x^2)-(x+3)

\int_{- 3}^{2} (9 - x^{2}) - (x + 3) d x

\frac{125}{6}

Decimal

20.83333 \dots

Solution steps

\int_{- 3}^{2} 9 - x^{2} - (x + 3) d x

Simplify

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

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

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

\int_{- 3}^{2} 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}

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What is the integral from-3 to 2 of (9-x^2)-(x+3) ?
The integral from-3 to 2 of (9-x^2)-(x+3) is 125/6