What is the integral from 0 to 4 of 1/((x-2)^3) ?

The integral from 0 to 4 of 1/((x-2)^3) is diverges

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integral from 0 to 4 of 1/((x-2)^3)

\int_{0}^{4} \frac{1}{( x - 2 ) ^{3}} d x

diverges

Solution steps

\int_{0}^{4} \frac{1}{( x - 2 ) ^{3}} d x

Find undefined (singularity) points:

x = 2

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_{0}^{2} \frac{1}{( x - 2 ) ^{3}} d x + \int_{2}^{4} \frac{1}{( x - 2 ) ^{3}} d x

\int_{0}^{2} \frac{1}{( x - 2 ) ^{3}} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int_{0}^{5} h (x) d x

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\int_{- 1}^{0} (e^{x}) d x

What is the integral from 0 to 4 of 1/((x-2)^3) ?
The integral from 0 to 4 of 1/((x-2)^3) is diverges