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- 4. Determine whether the improper integral converges and, if so, evaluate it. (If the quantity diverges, enter DIVERGES.) ∞ 04x dx(3 + x2)2 please show step by step clearly.Determine whether the improper integral ∞∫−∞dxx2+2x+8 converges or diverges?5. Determine whether the improper integral converges and, if so, evaluate it. ∞ 05x dx(3 + x2)2 PLEASE SHOW STEP BY STEP CLEARLY
- Suppose that f is an integrable function on R (real numbers). How do you show that the integral of f(x) exp(x2/k) converges to the integral of f(x) as k goes to infinity? Here exp() denotes the exponential function with base e.Determine whether integral 0 to pie /2 sec x dx converges or divergesdetermine all value/values of p for which the improper integral converges?