For each of the following improper integrals, note Why it

jernplate8 2021-09-16 Answered
For each of the following improper integrals, note Why it is omproper, and then set up the limit(s) that would be used to evaluate the integral.
\(\displaystyle{\int_{{-\infty}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}\)

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Expert Answer

lobeflepnoumni
Answered 2021-09-17 Author has 16251 answers
\(\displaystyle{\int_{{-\infty}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}\)
For the given integration the lower limit is infinity also, the integrand of the limit goes to infinity in the range of given integration at point x = -2.
Therefore, the given integral is improper.
Now to set up the integral:
\(\displaystyle{\int_{{-\infty}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}=\lim_{{{t}\rightarrow-\infty}}{\int_{{{t}}}^{{{4}}}}{\frac{{{3}}}{{{x}+{2}}}}{\left.{d}{x}\right.}\)
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