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

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

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

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

diverges

Solution steps

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{0}^{2 π} cos^{4} (t) d t

\int_{0}^{\frac{π}{4}} cos (2 t) d t

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x) - 5) d x

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

\int_{- 2}^{1} (\frac{1}{x ^{2}} - 5) d x

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