anonymous
  • anonymous
Determine whether the improper integral diverges or converges. evaluate integral if it converges: the integral from neg. infinity to pos. infinity of 4/(16+(x^2)) dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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TuringTest
  • TuringTest
the integrand is even so we can convert this to\[\int_{-\infty}^{\infty}\frac4{16+x^2}dx=2\int_{0}^{\infty}\frac4{16+x^2}dx\]\[=8\int_{0}^{\infty}\frac1{4^2+x^2}dx=8\lim_{n \rightarrow \infty}\int_{0}^{n}\frac1{4^2+x^2}dx\]which is going to give us an arctan thing...\[2\lim_{n \rightarrow \infty}\tan^{-1}(\frac x4)|_{0}^{n}=2\lim_{n \rightarrow \infty}\tan^{-1}(\frac n4)=\pi\]I hope I did that right!
TuringTest
  • TuringTest
oh good, wolfram agrees!
anonymous
  • anonymous
thanks!

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Akshay_Budhkar
  • Akshay_Budhkar
Yup its correct.. lol i actually solved to verify to see that u already verified using wolphram :P

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