Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Our community provides accurate and timely answers to help you understand and solve any issue.
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
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.
