What is the integral from-4 to 2 of x^{-3} ?

The integral from-4 to 2 of x^{-3} is diverges

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integral from-4 to 2 of x^{-3}

\int_{- 4}^{2} x^{- 3} d x

diverges

Solution steps

\int_{- 4}^{2} x^{- 3} d x

Find undefined (singularity) points:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 4}^{0} x^{- 3} d x + \int_{0}^{2} x^{- 3} d x

\int_{- 4}^{0} x^{- 3} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{3}^{4} 3 d x

What is the integral from-4 to 2 of x^{-3} ?
The integral from-4 to 2 of x^{-3} is diverges