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

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

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

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

\frac{2}{125}

Decimal

0.016

Solution steps

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

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

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

Integral of a constant:

\int a d x = a x

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

Simplify

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

= - [- \frac{1}{125} x]_{- 5}^{- 3}

Compute the boundaries:

- \frac{2}{125}

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

Simplify

= \frac{2}{125}

\frac{d}{d x} (- \frac{y ^{2}}{( x - y ) ^{2}})

2^{x^{2}}

\int \frac{1}{( x ^{2} + 2 ) ^{\frac{3}{2}}} d x

\int \frac{1}{x ^{2} + 8 x + 25} d x

x y^{^{'}} + (1 - x) y = 2 x e^{x}

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