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Calculus Level 1

Evaluate ∫ − 1 1 1 x 2 d x \large \int_{-1}^{1}\cfrac{1}{x^2}\;dx

0 -2 2 1 Diverges

James Watson by James Watson , 16, United Kingdom

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1 solution

Elijah L
Jul 6, 2020

Because there is a vertical asymptote at x = 0 x = 0 , the sum diverges and hence cannot be evaluated.

0 Helpful 0 Interesting 1 Brilliant 1 Confused

Of course , singularity occurs at x = 0 x=0 however we can calculate it by considering the Cauchy principal value as PV ⁡ ∫ − 1 ! 1 1 x d x = 0 \operatorname{PV}\int_{-1! }^1\frac{1}{x} dx= 0

Naren Bhandari - 10 months ago

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