Math 126 Name (Print): Block 1 Take-Home Due: 02/24/2017

Read Directions Entirely. By submitting this exam for a grade, you are agreeing to everything contained within.

This assignment is entirely optional. Your current score for Block 1 is: A = (Score on Test) + 14. Let B = (Score on this assignment). Your new score for Block 1 will be calculated as: Block 1 Score = A + .A(B−A

2 ).

Ex. If your test says 46, then A = 46 + 14 = 60. If you make a 100 on this assignment, then your Block 1 score is given by: Block 1 Score = 60 + .60( 100−60

2 ) = 72.

Play around with some number to see if you think it is worth your time to complete the assignment. It will be significantly harder than the in-class exam, but you have a week to complete it.

Feel free to use any sources you would like other than help from another person (discussions about how to approach a problem are fine, but you need to write out your own solutions from scratch). If the contents of your test contain work that leads me believe that you were directly and excessively working with other people, then I will submit it for academic misconduct.

Because this is a take-home assessment, the presentation of your solutions will be graded more strictly. You must show all work on each problem. You must write neatly, and the work must flow in a clear unambiguous manner, with more rigor than an in-class test. If your handwriting is terrible, you have the options of writing carefully or attaching a typed version of your solutions. I reserve the right to take away points simply because it looks sloppy or if the math syntax doesn’t quite make sense, even if I can guess what you mean (typically during in-class exams a little benefit of the doubt is given, due to the limited amount of time).

Grading will be done in ten point increments, i.e. 100, 90, 80, etc.

You must submit a stapled, printed copy to me by no later than the end of class on Friday, February 24, 2017.

Do not write graded material on this page.

Math 126 Block 1 Take-Home - Page 2 of 8 Due: 02/24/2017

1. For 0 ≤ x ≤ π 4

define the function

y =

√ˆ x 1 cos(t)dt−

ˆ sin(x) 1

tdt

Find y′. (Hint: Your final answer will have an integral in it)

2. Find the Arc Length of y = ln |sec(x)|, π 4 ≤ x ≤ π

2 . (Hint: trig identity, and pg. 328)

Math 126 Block 1 Take-Home - Page 3 of 8 Due: 02/24/2017

3. Find the total area between f(x) = sin(x), g(x) = cos(x), 0 ≤ x ≤ 2π. (Hint: will require three integrals)

4. Use even and odd functions to calculate

ˆ 2 −2

6 + 2x2 + 3x + 5x3 + 7x7 + x9 + x11dx

Math 126 Block 1 Take-Home - Page 4 of 8 Due: 02/24/2017

5. Evaluate ˆ 2 0 x9

√ x5 + 7dx

6. A spring is naturally 20m long. It takes a force of 10N to stretch the spring to 40m. Find the amount of work done compressing the spring to 10m.

Math 126 Block 1 Take-Home - Page 5 of 8 Due: 02/24/2017

7. An object is formed taking the bounded region described by y = ex−1 + 1, y = 1 x = 0, x = 1 and rotating it around the line y = 1. Find the volume of the object (Disk).

8. How much work is done lifting a car weighing 16000N up 100m with a cable that that weighs .5N m

.

Math 126 Block 1 Take-Home - Page 6 of 8 Due: 02/24/2017

9. An object is formed taking the bounded region described by y = x2 + 1, y = 5 and rotating it around the x−axis. Use the Washer Method to find the volume of the object.

Math 126 Block 1 Take-Home - Page 7 of 8 Due: 02/24/2017

10. An object is formed taking the bounded region described by y = x2 + 1, y = 5 and rotating it around the x−axis. Use the Shell Method to find the volume of the object. (Hint: will require two integrals)

Math 126 Block 1 Take-Home - Page 8 of 8 Due: 02/24/2017

11. An object An object is formed taking the function y = x 1 3 , 0 ≤ x ≤ 27 and rotating it around

the x−axis. Find the surface are of the object.