What is the integral from 0 to 2 of (x+2)(x-3) ?

The integral from 0 to 2 of (x+2)(x-3) is -34/3

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integral from 0 to 2 of (x+2)(x-3)

\int_{0}^{2} (x + 2) (x - 3) d x

- \frac{34}{3}

Decimal

- 11.33333 \dots

Solution steps

\int_{0}^{2} (x + 2) (x - 3) d x

Expand

(x + 2) (x - 3) : x^{2} - x - 6

= \int_{0}^{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_{0}^{2} x^{2} d x - \int_{0}^{2} x d x - \int_{0}^{2} 6 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

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

\int_{0}^{2} 6 d x = 12

= \frac{8}{3} - 2 - 12

Simplify

\frac{8}{3} - 2 - 12 : - \frac{34}{3}

= - \frac{34}{3}

What is the integral from 0 to 2 of (x+2)(x-3) ?
The integral from 0 to 2 of (x+2)(x-3) is -34/3