What is the integral from-2 to 3 of (x+2)-(x^2-4) ?

The integral from-2 to 3 of (x+2)-(x^2-4) is 125/6

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integral from-2 to 3 of (x+2)-(x^2-4)

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

\frac{125}{6}

Decimal

20.83333 \dots

Solution steps

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

\int_{0}^{2} 12 d x

\int_{0}^{5} 2 t e^{- t^{2}} d t

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

\int_{1}^{5} (\frac{x}{5} + \frac{y}{20}) d y

\int_{- 3}^{6} 3 x - 5 d x

What is the integral from-2 to 3 of (x+2)-(x^2-4) ?
The integral from-2 to 3 of (x+2)-(x^2-4) is 125/6