In this question, you wil use a substitution to carry out the following integration: (x' + 2) Ar de In this question, you will estimate the value of the integral If the answer re ion, enter it as c. re- dx a. The integral involves the companie function (* + 2). when one u - g(x) = using three different approximations du b. Find the derivative dor . Subdivide the interval [1,4] into three sub-intervals of equal width and complete the following: du Ax = dr - Transform the original olving a by using the subs s of 9 (: ) in the Integral by U. Replace 9 ' (2) dix by du ( equivalent dr a2 f( a2 ) y replace dr by du (x' + 2) " Ax de a3= 1(83) du X1= 1( * 1 ) (you do not need to enter du in your answer) . Carry out the integration, and find the most general ar tvative (in terms of u). f ( * 2 ) " X3 = f( x3 ) = Finaly, newthe your answer in terms of * by replacing w by p(). b. Calculate the approximate value of the integral using the trapezoidal rule. (x' + 2)" Ar de Area ~ c. Calculate the approximate value of the integral using the midpoint rule. Ummbake Toingiting hop Area ~ . Calculate the approximate value of the integral using Simpson's rule. Area ~ . It is possible to show that an antiderivative of x e"*/3 is (12 Points] DETAILS -3(x +3) e -3 Integrate each of the fo ing functions using substitution, finding the most general antiderivative. Also enter u, the function of x that you substitute. Using this antiderivative, calculate the exact value of the integral. If your answer requires a constant of integration, enter it as c. Integral = 5r +2 VI +2r+4 4. [-/4 Points] DETAILS In this question, you will investigate whether the improper integral 72 d converges or diverges. If it converges, you will find its value. a. Calculate the value of the integra where b is a finite number whose value is greater than one. Value = b. Does the value of the integral approach a limit as b tends to infinity? If so, enter this limiting value: 72 dx "symbolic formatting help