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anonymous
 4 years ago
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
anonymous
 4 years ago
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

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1the 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
 4 years ago
Best ResponseYou've already chosen the best response.1oh good, wolfram agrees!

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.1Yup its correct.. lol i actually solved to verify to see that u already verified using wolphram :P
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