MATH3503 Online Assignment 103

• 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)
  • Exponential and logarithmic functions with base e: exp(x) (`=e^x`), ln(x) (or log(x))
  • Square root: sqrt(x)
  • Absolute value: abs(x)

Quiz 3. November 12, 2020

1.  
   \(\displaystyle\int \sin^{3}(4x)\cos^{9}(4x)\,dx\)
   = \( + C\)
     * Use cosine only, and enter `cos^n x` as cos(x)^n.
   
   
2.  
   \(\displaystyle\int\frac{4x+2}{x^2-8x+15}\,dx\)
   = \( + C\)
   
   
   
3.  
   \(\displaystyle\int \sqrt{x^2 + 8x+20\,}\,dx\) `= int`  \(dt\)
   Use trigonometric substitution so that the integral is in terms of a single trigonometric function, `sin(t)`, `cos(t)`, `tan(t)`, or `sec(t)`.
   
   
4.  
   \(\displaystyle\int\frac{4x^2+3x+14}{(x^2+2)(x-1)}\,dx\)
   = \( + C\)
   
   
   

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