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

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

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Compute the indefinite integral:

\int \frac{1}{x ^{2}} d x = - \frac{1}{x} + C

Compute the boundaries:

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

= 0 - (- \frac{1}{3})

Simplify

= \frac{1}{3}

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