Step 1

Write the definition of the improper integrals.

Improper integrals are definite integrals that cover an unbounded area.

For example,

\(\displaystyle\int{\left\lbrace{1}\right\rbrace}^{{\propto}}{\frac{{{1}}}{{{x}^{{{2}}}}}}{\left.{d}{x}\right.}\)

Step 2

Now, solve the above integral.

\(\displaystyle{\int_{{{1}}}^{{\propto}}}{\frac{{{1}}}{{{x}^{{{2}}}}}}{\left.{d}{x}\right.}={{\left[-{\frac{{{1}}}{{{x}}}}\right]}_{{{1}}}^{{\propto}}}\)

=0-(-1)

=1

Hence.

Write the definition of the improper integrals.

Improper integrals are definite integrals that cover an unbounded area.

For example,

\(\displaystyle\int{\left\lbrace{1}\right\rbrace}^{{\propto}}{\frac{{{1}}}{{{x}^{{{2}}}}}}{\left.{d}{x}\right.}\)

Step 2

Now, solve the above integral.

\(\displaystyle{\int_{{{1}}}^{{\propto}}}{\frac{{{1}}}{{{x}^{{{2}}}}}}{\left.{d}{x}\right.}={{\left[-{\frac{{{1}}}{{{x}}}}\right]}_{{{1}}}^{{\propto}}}\)

=0-(-1)

=1

Hence.