MATH 100 - Fall 2012Homework #C - Section 5.2We will not collect this assignment, butit will help you prepare for thethird midterm on Thursday, November 15th.We will post solutions onmoodle by November 12th.Note:When computing antiderivatives, you can always check your answer, so you canbe sure it is correct. This is very useful in exams.1. Let’s warm up with some easier antiderivatives.Zx3dxZ√x dxZ1x3dxZ(x3-2x2+ 7x-5)dxZsinx dxZcosx dxZexdxZsec2x dx2. The poor integralZ1xdxis often misunderstood. Let’s get to know her a bit better.(a) Calculate the domain and the derivative ofF1(x) = lnx.(b) Calculate the domain and the derivative ofF2(x) = ln(-x).(c) Calculate the domain and the derivative ofF3(x) = ln|x|.(d) In view of the above, what isZ1xdx?(e) Calculate the derivative ofF4(x) = ln(2x). Do we have a problem?