MATH3503 Online Assignment 202

• Make sure to use the link on the Learning Hub, which contains a user name and a user ID unique to you, otherwise your mark would not be recorded. You may use the URL without '?uname=...&uid=...' if you just want to practice. You will get different numbers every time you open the page.
• Numerical answers are evaluated as correct if the difference from the correct value is less than `0.001 times` (correct value) unless otherwise specified. That means, you need to keep at least 4 significant digits (e.g., 12.34, 0.01234, etc.) in your final answer, and a couple of more digits in the intermediate steps.
• Arithmetic operators:

  Multiplication	* (You cannot omit it!)
  division	/

• Available functions
  • Trigonometric functions: sin(x), cos(x), tan(x), sec(x), asin(x), acos(x), atan(x)
  • Exponential and logarithmic functions with base e: exp(x) (`=e^x`), ln(x) (or log(x))
  • Square root: sqrt(x)
  • Absolute value: abs(x)

Midterm 2 (Take home test) due on November 26, 2020

1. It is an open-book exam. However, you are not allowed to consult with anyone else.
2. Please sign the "assessment declaration" form in "Midterm 2" folder under Activities > Assignments.
3. Your hand-written work should be written legibly and in a well-organized manner on blank sheets of paper (or iPad, etc.). You need to show steps leading to the solution.
4. Submit your hand-written work (single PDF if possible) to the folder "Midterm2".
5. Note that a correct answer online without hand-written work will be given zero marks.

1. Compute  
   \(\displaystyle\int_0^x \frac{dx}{2x^2 + 3x + 3}\)
   =
   
   
   
2. Compute  
   \(\displaystyle\int_0^x \frac{dx}{7x^2 -56x + 105}\)
   =
   
   
   
3. Compute  
   \(\displaystyle\int_0^x \frac{\sin^7(\sqrt[7]{5x+0.2})}{\sqrt[7]{(5x+0.2)^{6}\,}}dx\)
   =
   
   
   
4. Compute the length of the curve
     \(\displaystyle 5y^2 = 2(x-7)^3\)   for \(7\le x \le 10\). Arc length = *Enter a decimal number with more than 4 significant digits.
   
   
5. Compute the surface area of the ellipsoid (like a rugby ball) obtained by rotating the following ellipse about the `x`-axis:
   \(\displaystyle \frac{x^2}{16} + \frac{y^2}{9} = 1\) Surface area = *Enter a decimal number with more than 4 significant digits.
   
   
   

If you are ready to submit the result, click Submit!   *Make sure that all questions are evaluated. Click "Check answers!" before clicking "Submit!".