please be as specific as possible, will rate up!! and please ONLY use one of the followingmethods for integration. (important)?? Algebraic Techniques likecompleting the square, longdivision, etc; (Section 8.1) ? Substitution; (Section 5.6)? ??? ?Integration by parts; (Section 8.2) Trigonometric integrals andidentities or substitutiontechniques used to solve them; (Section 8.3)Trigonometric substitution; (Section 8.4)Partial fractions; a n d Improper integrals

With the tools of double integration, you can now revisit some previously thought impossible single variable integrals and evaluate them. Consider the improper integral Co 0-2x _ -6x I = which you are told converges. In fact, I = In(3). (a) Determine a function f(x, y) such that f, f(x, y)dy = . Verify your result by directly showing the integration. (b) Use part (a) to rewrite the above single integral as a double integral. (c) Reverse the order of integration in part (b) and evaluate the double integral to obtain the desired result. Even though change of order has so far been restricted to bounded regions, you can assume the results holds for (strongly) convergent integrals over unbounded regions. For all parts of this question: See announcement on integral expectations. Be especially careful in this question not to use outside techniques like Frullani integrals or Feynman's trick. Make especially sure to follow steps (a) - (c)