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Sagot :
Integration is the process of finding integral. The value of the integration [tex]\int_{{{0}}}^{{\infty}}}{\dfrac{{{\left.{d}{x}\right.}}}{{{\left({x}+{9}\right)}^{{{2}}}}}}\)\\[/tex] converges.
What is integration?
Integration is the process of finding integral. Integral help us to describe the function of area, volume, and other such concepts.
Given to us
[tex]\int_{{{0}}}^{{\infty}}}{\dfrac{{{\left.{d}{x}\right.}}}{{{\left({x}+{9}\right)}^{{{2}}}}}}\)\\[/tex]
To know whether the internal will converge or diverge, we will solve the integral,
[tex]\int_{{{0}}}^{{\infty}}}{\dfrac{{{\left.{d}{x}\right.}}}{{{\left({x}+{9}\right)}^{{{2}}}}}}\)\\\\\\ =[ -\dfrac{1}{x+9}]_0^\infty\\\\= \dfrac{1}{9}\\\\= 0.\overline{1}[/tex]
As we can see that the value of the integration [tex]\int_{{{0}}}^{{\infty}}}{\dfrac{{{\left.{d}{x}\right.}}}{{{\left({x}+{9}\right)}^{{{2}}}}}}\)\\[/tex] converges toward zero, therefore we can say that the given integration converges.
Hence, the value of the integration [tex]\int_{{{0}}}^{{\infty}}}{\dfrac{{{\left.{d}{x}\right.}}}{{{\left({x}+{9}\right)}^{{{2}}}}}}\)\\[/tex] converges.
Learn more about Integration:
https://brainly.com/question/18651211
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