How do you determine if the improper integral converges or diverges #int 8dx/(x^(2)+1)# from 1 to infinity?
I assume (despite the 8) you want to know if
By signing up, you agree to our Terms of Service and Privacy Policy
To determine if the improper integral [ \int_{1}^{\infty} \frac{8 , dx}{x^2 + 1} ] converges or diverges, follow these steps:

Evaluate the indefinite integral: [ \int \frac{8}{x^2 + 1} , dx = 8 \arctan(x) + C ]

Evaluate the definite integral from 1 to ( t ): [ \int_{1}^{t} \frac{8 , dx}{x^2 + 1} = 8 \left[\arctan(t)  \arctan(1)\right] ] [ = 8 \left[\arctan(t)  \frac{\pi}{4}\right] ]

Determine the limit as ( t ) approaches infinity: [ \lim_{{t \to \infty}} 8 \left[\arctan(t)  \frac{\pi}{4}\right] ]

If the limit exists and is finite, the improper integral converges. If the limit does not exist or is infinite, the improper integral diverges.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you use the Nth term test on the infinite series #sum_(n=1)^ooe^2/n^3# ?
 How do you show whether the improper integral #int e^x/ (e^2x+3)dx# converges or diverges from 0 to infinity?
 How do you determine if the improper integral converges or diverges #int_0^oo 1/ (x2)^2 dx #?
 How do you determine if #Sigma (7^n6^n)/5^n# from #n=[0,oo)# converge and find the sums when they exist?
 How do you determine the convergence or divergence of #Sigma ((1)^(n+1)n)/(2n1)# from #[1,oo)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7