Please provide justification for each step:

Also, I am hiring a person who can work together for this semester for Calc 2.

1. Evaluate the following antiderivatives. I. sin (x) cos'(x) dr II. sec (x) tan (x) da III. zell + rear dx IV. cos( VT) dr 2. Calculate the integrals below. A. sin ?(2x) + (72 +6)3 4r B. 2rvAr + 1dr C. sec5 (r) tan ?(r) dr D. In(z) da 3. Determine if the arguments below are correct or not. If the argument is incorrect, identify all of the errors made and then give the correct argument argument. I. Let u = 2r + 1. Then, ha +12 de = du = 2Inlul =2In(e) - 2In(1) = 2. II. Using integration by parts we find: asin(x) dx = -roos(z) + cos(x) dx = -rcos(z) + sin(z) -cos(x). 4. The solid S is formed by revolving the region bounded by y = vi, y = 0, and z = 9 about the line y = -1. Calculate the volume of S. Simplify your final answer. 5. The region R is bounded by y = 2 + 2, y = 8, x = 0 and r = 2. Suppose R is revolved about the line * = 3 to form a solid of revolution. i. Use the washer method to set up, but do not evaluate, an integral or sum of integrals that gives the volume of the solid. ii. Use the shell method to set up, but do not evaluate, an integral or sum of integrals that gives the volume of the solid. 6. Find a function f(x) so f(0) = 1 and the length of the curve segment y = f(x) from r = 0 to = = 1 is given by V1 + 9 sin? (2x) da