## Study23 Group Title RHS HELP!!! (Reimann Sums) (Note that I have NOT learned about integrals yet) Here's the Q: I'm given a curve where 0<=x<=10, and there are 5 rectangles, so n=5. I calculated delta x to be 2. I'm really confused how to use these two formulas to find both the LHS and the RHS. I've typed the two formulas below, in my reply. Please help!! I AM REALLY CONFUSED! Thank you! one year ago one year ago

1. Study23 Group Title

$\ \huge \text {LHS:} \sum_{i=0}^{n-1} f(x_i) Δ x$

2. Study23 Group Title

$\ \ \huge \text {RHS:} \sum_{i=1}^{n} f(x_i) Δ x$

3. hamza_b23 Group Title

well delta x = (b-a)/n

4. hamza_b23 Group Title

5. khoala4pham Group Title

6. Study23 Group Title

$$\ \Huge \text{Oh, and: } x_i = a+iΔx$$

7. hamza_b23 Group Title

if you just started integrals you shouldve went over sigma notation im pretty sure, and you just expand it

8. khoala4pham Group Title

This isn't helpful without the function. Otherwise the answer will be just theoretical stuff.

9. Study23 Group Title

I don't have a function value... I'm only given a graph in my textbook and am told to find the lower estimate and an upper estimate.

10. Study23 Group Title

And, we haven't even discussed what an integral is in class...

11. khoala4pham Group Title

Could you give a description of what your graph is?

12. Study23 Group Title

It looks something like:|dw:1360464858577:dw|

13. Study23 Group Title

My confusion is I'm not sure how to use the two summation equations....

14. Study23 Group Title

And then use the values I know from the graph

15. khoala4pham Group Title

Okay, that's better. Well you first need to partition the interval into 5 equal intervals. For the left Riemann: for your values x = 0,2,4,6,8, draw a vertical line that TOUCHES the graph of the function. This vertical line is the height of the rectangle that you are estimating the curve with. Each rectangle's width is 2. |dw:1360465074815:dw| For the right hand do the same except for now, use let the x values be x = 2,4,6,8,10 |dw:1360465192357:dw|

16. khoala4pham Group Title

Note how the left hand Riemann is an underestimation of area while the right hand Riemann is an over estimation of area.

17. Study23 Group Title

@khoala4pham How do I use the sigma equations? Where do they come into this?

18. Study23 Group Title

Anyone??

19. khoala4pham Group Title

The sigma equations represent area. They mean that you sum up the areas of each individual rectangle. That is all that they mean. For the left hand Riemann, you take 2*(f(0) + f(2) + f(4) + f(6) + f(8)) For the right, 2*(f(2) + f(4) + f(6) + f(8) + f(10)) Why that though? Because for the RHR, the first rectangle has height f(0) and its width is 2. The second rectangle has height f(2) and width 2. So forth and so on.

20. Study23 Group Title

How do you know to choose 0,2,4,6,8 and 2,4,6,8,10?

21. khoala4pham Group Title

Well your a is zero in this case. a is the place where your interval begins. From your equation of the left hand Riemann, you see that x_i = a + i*(deltax) i runs from 0 to n-1. Well, n here is 5--the domain is partitioned into 5 intervals. That means that i = 0,1,2,3,4. Consequently x will be x = 0 + 2(0), 0 + 2(1), 0+2(2),0+2(3),0+2(4) x = 0,2,4,6,8. The same applies to the right Riemann.

22. Study23 Group Title

THAT MAKES SO MUCH MORE SENSE! THANK YOU, @khoala4pham! I was getting confused with the $$\ \Huge \sum \text{ notation!}$$

23. khoala4pham Group Title

The notation is highly ambiguous if you are not used to it. The x_i is a number. Deltax is also a number. You are summing numbers across indexes. How you found your index is obtained above.

24. Study23 Group Title

Can you explain the RHS for "Well your a is zero in this case. a is the place where your interval begins. From your equation of the left hand Riemann, you see that x_i = a + i*(deltax) i runs from 0 to n-1. Well, n here is 5--the domain is partitioned into 5 intervals. That means that i = 0,1,2,3,4. Consequently x will be x = 0 + 2(0), 0 + 2(1), 0+2(2),0+2(3),0+2(4) x = 0,2,4,6,8. The same applies to the right Riemann." I dont really understand the RHS...

25. Study23 Group Title

How you got the numbers 2,4,6,8,10

26. Study23 Group Title

If i runs from 1 to n, so that means i runs 1 to 5...

27. Study23 Group Title

I'm getting like 2, 5 ...? x_1= (a=0) + (1)(delta x = 2) = 2 x_2 = (a=1) + (2)( delta x = 2) =5

28. Study23 Group Title

@khoala4pham Why do you keep 0 constant? Consequently x will be x = 0 + 2(0), 0 + 2(1), 0+2(2),0+2(3),0+2(4) x = 0,2,4,6,8.

29. khoala4pham Group Title

your equation of x_i = a + i*(delta x). a = 0 by default. a is the value that you start your interval with. if your interval were from (20,50) then a = 20. If your interval were (-3,24), then a = -3. In your initial problem you told me that 0 <= x < = 10. Thus a = 0.