What is the integral from 0 to 2 of 2/(x^2) ?

The integral from 0 to 2 of 2/(x^2) is diverges

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integral from 0 to 2 of 2/(x^2)

\int_{0}^{2} \frac{2}{x ^{2}} d x

diverges

Solution steps

\int_{0}^{2} \frac{2}{x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: [- \frac{1}{x}]_{0}^{2}

= 2 [- \frac{1}{x}]_{0}^{2}

Compute the boundaries:

diverges

= diverges

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

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