What is the integral from 3 to 7 of (x-3)(x+6) ?

The integral from 3 to 7 of (x-3)(x+6) is 280/3

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integral from 3 to 7 of (x-3)(x+6)

\int_{3}^{7} (x - 3) (x + 6) d x

\frac{280}{3}

Decimal

93.33333 \dots

Solution steps

\int_{3}^{7} (x - 3) (x + 6) d x

Expand

(x - 3) (x + 6) : x^{2} + 3 x - 18

= \int_{3}^{7} x^{2} + 3 x - 18 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}^{7} x^{2} d x + \int_{3}^{7} 3 x d x - \int_{3}^{7} 18 d x

\int_{3}^{7} x^{2} d x = \frac{316}{3}

\int_{3}^{7} 3 x d x = 60

\int_{3}^{7} 18 d x = 72

= \frac{316}{3} + 60 - 72

Simplify

\frac{316}{3} + 60 - 72 : \frac{280}{3}

= \frac{280}{3}

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What is the integral from 3 to 7 of (x-3)(x+6) ?
The integral from 3 to 7 of (x-3)(x+6) is 280/3