Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer. | In |x| dx -3 Choose the correct answer below. O A. By integration, the integral has a finite value, so the integral converges. B. By integration, the integral does not have a finite value, so the integral diverges. OC. f(x) is not a finite limit. By the Limit Comparison Test, the integral diverges because lim X-00 9(x) OD. By the Direct Comparison Method, the integral converges because In |x| dx converges and In |x| dx converges.

2) Determine whether the integral converges or diverges. Justify your answer in each case using proper integral and limit notation. If the integral converges, find its exact value. 10 dx 3√x

Use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integral for convergence. If more than one method applies, use whatever method you prefer. S dx O B. √xº Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. The comparison function g(x)= can be used with a comparison test to determine convergence, but since 1 3 x° +6 OA. 00 dx S 0 √x +6 √√x +6 this choice of g(x) is discontinuous at x = OF dx dx By the Direct Comparison Test, the integral diverges because f(x) √√x+6 and g(x) are both continuous and positive over the interval, f(x) > g(x) over this interval, and the integral of g(x) over this interval diverges. (Type your answer in interval notation.) 1 this choice of g(x) is discontinuous at x = dx dx izlas -S. √√x+6 S 0 √√x +6 1 The comparison function g(x)= can be used with a comparison test to determine convergence, but since S interval converges, and J 1 ndj- dx √√x+6 (Type your answer in interval…