What is the integral from-3 to-5 of (-4)^{-3} ?

The integral from-3 to-5 of (-4)^{-3} is 1/32

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integral from-3 to-5 of (-4)^{-3}

\int_{- 3}^{- 5} (- 4)^{- 3} d x

\frac{1}{32}

Solution steps

\int_{- 3}^{- 5} (- 4)^{- 3} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 5}^{- 3} (- 4)^{- 3} d x

Integral of a constant:

\int a d x = a x

= - [(- 4)^{- 3} x]_{- 5}^{- 3}

Simplify

- [(- 4)^{- 3} x]_{- 5}^{- 3} : - [- \frac{1}{64} x]_{- 5}^{- 3}

= - [- \frac{1}{64} x]_{- 5}^{- 3}

Compute the boundaries:

- \frac{1}{32}

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

Simplify

= \frac{1}{32}

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What is the integral from-3 to-5 of (-4)^{-3} ?
The integral from-3 to-5 of (-4)^{-3} is 1/32