What is the integral from 9 to 24 of (-x+12) ?

The integral from 9 to 24 of (-x+12) is -135/2

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integral from 9 to 24 of (-x+12)

\int_{9}^{24} (- x + 12) d x

- \frac{135}{2}

Decimal

- 67.5

Solution steps

\int_{9}^{24} - x + 12 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_{9}^{24} x d x + \int_{9}^{24} 12 d x

\int_{9}^{24} x d x = \frac{495}{2}

\int_{9}^{24} 12 d x = 180

= - \frac{495}{2} + 180

Simplify

- \frac{495}{2} + 180 : - \frac{135}{2}

= - \frac{135}{2}

What is the integral from 9 to 24 of (-x+12) ?
The integral from 9 to 24 of (-x+12) is -135/2