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

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

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

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

diverges

Solution steps

\int_{0}^{3} \frac{1}{x - 2} 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} d x + \int_{2}^{3} \frac{1}{x - 2} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

x, 2 x 81 - x^{2}

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

\int 12 x^{2} - 6 x + 1 d x

y^{^{''}} - 3 y^{^{'}} = 9 t, y (0) = 3, y^{^{'}} (0) = 0

\frac{x}{y} + \frac{y}{x} = 3 πa b^{2}

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