What is the integral from-3 to-2 of (2-x)/(32) ?

The integral from-3 to-2 of (2-x)/(32) is 9/64

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integral from-3 to-2 of (2-x)/(32)

\int_{- 3}^{- 2} \frac{2 - x}{32} d x

\frac{9}{64}

Solution steps

\int_{- 3}^{- 2} \frac{2 - x}{32} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{32} \cdot \int_{- 3}^{- 2} 2 - x 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

= \frac{1}{32} (\int_{- 3}^{- 2} 2 d x - \int_{- 3}^{- 2} x d x)

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

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

= \frac{1}{32} (2 - (- \frac{5}{2}))

Simplify

\frac{1}{32} (2 - (- \frac{5}{2})) : \frac{9}{64}

= \frac{9}{64}

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What is the integral from-3 to-2 of (2-x)/(32) ?
The integral from-3 to-2 of (2-x)/(32) is 9/64