MATH3503 Online Assignment 2

• 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.

Definite Integrals

1.  
   `int_{-7}^3 8 x^2 dx =`
   
   
2.  
   `int_{6}^8 3\ dt =`
   
   
3.  
   `int_{-5}^6 dq =`
   
   
4.  
   `int_{6}^{8}(x+3)^2 dx =`
   
   
5.  
   `int_{-12}^{-7}(t^2-6t+ 3 ) dt =`
   
   
6.  
   `int_{0}^{9}7(6p-2 )^15 dp =`
   *Hint: What is the derivative of `(ax+b)^n`? Enter `1.2345\times 10^{67}` as 1.2345E+67
   
   
7.  
   `int_{7}^{10}(2dr)/r^{6} =`
   *Enter `1.2345\times 10^{-67}` as 1.2345E-67
   
   
8.  
   `int_{2}^{6}(6x^2 + 3/x^5) dx =`
   
   
9.  
   `int_{-1}^{3}(x^2 -8x + 15)/(x-3) dx =`
   *Hint: Simplify the integrand by factoring the numerator.
   
   
10.  
    `int_{1}^{6}(6/x +9/x^{1.03}) dx =`
    
    
    
11.  
    Find the area under the curve `y = 8(1+sin(9x))` from `x=7` to `x=3`
    Area =
    * Plot the graph using, e.g., https://www.desmos.com/calculator.
    
    
12.  
    Waste water is flowing into a tailings pond at the rate of `r(t) = 2(1+t)^{-1.7}` \(\text{m}^3/\text{sec}\).

    1. Find the total volume `V(t)` of the water in the tailings pond at time `t`, given that `V(0)= 0`.
       ` V(t) = `
    2. After a long time what will be the volume of water? I.e., `V(\infty) = `
       *Hint: `infty+`constant `=infty`,  \(1/\infty = 0\)
    
    
13.  
    When the brake is applied, a car's speed decreased exponentially: \(v(t) = 7e^{-t/4}\).

    1. Find the position `x(t)` at time `t`, given that `x(0)=3`.
       ` x(t) = `
    2. Where does the car eventually stop? I.e., `x(\infty)=`
       *Hint: constant`times infty = infty`,  `exp(-infty)=0`
    
    

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