Question

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!

Answer 1

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

Answer 2

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

Answer 3

well delta x = (b-a)/n

Answer 4

and what is your f(x)?

Answer 5

I'm not sure what you're asking. I need your function value.

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

Could you give a description of what your graph is?

Answer 12

It looks something like:

Answer 13

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

Answer 14

And then use the values I know from the graph

Answer 15

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.



For the right hand do the same except for now, use let the x values be x = 2,4,6,8,10