What is the integral from-5 to-7 of (-5)^{-3} ?

The integral from-5 to-7 of (-5)^{-3} is 2/125

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integral from-5 to-7 of (-5)^{-3}

\int_{- 5}^{- 7} (- 5)^{- 3} d x

\frac{2}{125}

Solution steps

\int_{- 5}^{- 7} (- 5)^{- 3} d x

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

= - \int_{- 7}^{- 5} (- 5)^{- 3} d x

Integral of a constant:

\int a d x = a x

= - [(- 5)^{- 3} x]_{- 7}^{- 5}

Simplify

- [(- 5)^{- 3} x]_{- 7}^{- 5} : - [- \frac{1}{125} x]_{- 7}^{- 5}

= - [- \frac{1}{125} x]_{- 7}^{- 5}

Compute the boundaries:

- \frac{2}{125}

= - (- \frac{2}{125})

Simplify

= \frac{2}{125}

\frac{d}{d x} (\frac{2}{5} x^{5} - 3 x^{2} + 8 x - 5)

y = csc^{2} (x) - 2

5 y^{^{''}} + y^{^{'}} = 0

y^{^{'}} = sin (3 x)

\frac{d}{d x} (ln (cos (0)))

What is the integral from-5 to-7 of (-5)^{-3} ?
The integral from-5 to-7 of (-5)^{-3} is 2/125