Can you help me with these questions about improper integrals

In each part, determine all values of p for which the integral is improper. Enter in interval notation or "none" if there are no relevant values of p. (a) p values that make integral improper O 5 ( b ) 2 x - p p values that make integral improper O (c) e PX da 6 p values that make integral improperEvaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. +00 2:3695a d2 = f, C] The integral 0 10 f a a + 2:) is improper for two reasons: the interval [0, 00] is infinite and the integrand has an infinite discontinuity at a: = 0. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows: 0\" 1 1 1 0 1 f 0 d9; = f 0 d3 +f 0 d3 0 (1+:c) n (1+a:) 1 (1+a:) If the improper integral diverges, type an upper-case "D". C] x In(x) dx a. Find the values of p for which the integral converges. The integral converges for all values of p in the interval: b. For the values of p at which the integral converges, evaluate it. x" In(x) da =For each of the following integrals, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition. (To indicate convergence or divergence, enter one of the words converges or diverges in the appropriate answer blanks.) e 2. J1 23146 dae : a similar integrand is so we predict the integral da : a similar integrand is so we predict the integral x348x+6 dax : a similar integrand is so we predict the integral 2+6 2346x2+6 dx : a similar integrand is so we predict the integralEvaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. de =[1 point} In the graph below, the function ax) is graphed with a bold, blue curve, and the function g(::) with a light, red curve. Assume that the behavior of both functions as a: > 00 is accurately suggested by the domain on which they are graphed in the figure. '5': Suppose I: f(:c) dz: converges. What does this graph suggest about the convergence of few g(;t:) (12:? O A. few 9(3) d3: neither converges nor diverges O B. 1:0 9(3) (13: converges O C. the graph does not provide enough information to suggest with any certainty whether 1:0 9(w) da: converges or diverges O D. [00 0(3) do; diverqes Consider the integral 2 1 / Dx+30 0 233 If the integral is divergent, type an uppercase "D". Otherwise, evaluate the integral. Cl