Riemann sums

Riemann sums

1. 1. First you need to know your x values and the amount of rectangles you’ll use (n)

   • 2. After knowing the values of your x and n you need to get the ∆x this using the formula of ∆x=(b-a)/n with b and a being your values for x1 and x2.
     • 3. Then you graph with all the elements that the problem gives you (the function, the integration limits, and your ∆x)
       • 4. Followed by a value table where you can get the intersection point for your curve
         • 5. After that you decide which side use
           • A) Left-endpoints: You need to start your x1 with the value of it. For example if your x1 is 0 you star counting your ∆x from there and you add that value the amount of times of your n and the value must approach the value of x2
           • C) Middle-endpoints: You need to start your x1 with the value of x_1+∆x/2 this because you are always going to use the values of the middle of your graph. For example if your x1 is 0 and your ∆x=.1 you star counting your ∆x from 0.05 and you add that value the amount of times of your n and the value must approach the value of x2.
           • B) Right-endpoints: You need to star your x1 with the value of x_1+∆x this because you are always going to use the values of the right corner. For example if your x1 is 0 and your ∆x=.1 you star counting your ∆x from 0.1 and you add that value the amount of times of your n and the value must approach the value of x2
           • 6. Then you solve the function based on the values of your n or in other words your value taking into consideration ∆x and you add all of them (the amount of n are going to be the amount of rectangles)
           • 7. After adding all the values you multiply the result bye the value of ∆x
           • 8. You express the result with u^2