You are encouraged to work on this assignment collaboratively with your peers in class. You can also ask me for hints if you are stuck. Yet you should write up your own work and submit it on Canvas in ONE pdf file. Show all of your work for full credit, and your work should be clearly written and organized. The homework is about 7.6, 7.7, and 7.8. Problem 1. Evaluate the indefinite integral / o2 In z dr using integration by parts and (a) picking u = In x (following our LIPET test). (b) picking u = * (not following our LIPET test). Hint: That is, dv = Inx dz. We do know what is the integral of Inx from lecture. Find that out. Problem 2. Evaluate the definite integral In x VI dx. Hint: Can we apply the FTC part 1 right off the bat? Why or why not?Problem 3. An improper integral f (z) dr is called absolutely convergent if / | f(x)| dz converges. It can be shown that if an mtegra] is absolutely convergent, then it is convergent. Your task is to show that " dy is absolutely convergent. 1 Hint: Recall the trick you did in MTH 251 while learning the Squeeze theorem. What is the range of sin #? Once you figure that out, what about the range of | sin x|? Problem 4. Estimate / f(x) dx by computing M3, 73, and So for a function f taking on the values in the following table: 2 2.5 3 3.5 4 4.5 5 f(x) 2 2 1 0 10 1 09 - 4 -2 Hint: Pay attention to the little subscripts