Question

Somebody please help!!

Calculate the left Riemann sum for the given function over the given interval using the given value of n. f(x)= 2-6x over [-1,1] ; n=4

Answer 1

anybody?

Answer 2

Just do it.

With n = 4, [-1,1] is chopped up into [-1,-1/2][-1/2,0][0.1/2][1/2,1]

The LEFT Riemann Sum requires f(-1), f(-1/2), f(0), and f(1/2).

Evaluate away!

Answer 3

You are building rectangles. That's all.

With n = 4 on [-1,1], the width of each rectangle is 1/2.

The height of each rectangle is given bu the function evaluations suggested above.

Rectangles. That's it. We'll complicate it with trapezoids later. For now, it's just rectangles. Length * Width. Done.

Answer 4

is there a specific formula I have to use?

Answer 5

Yes. The formula for the area of a rectangle. Use it four times with n = 4.

Answer 6

how do I determine width and height? I am so lost

Answer 7

Did you not read the previous posts? I'm not going to do it for you, although I nearly have. You are going to have to think through it.

Interval: [-1,1]
Sub-Intervals: n = 4
Define Sub-Intervals: [-1,-1/2][-1/2,0][0.1/2][1/2,1]
Width of Sub intervals: 1/2 (Since 1-(-1) = 2 and 2/4 = 1/2

Width of EACH rectangle: 1/2 - Every time.
Height of the four rectangles: f(left-most value for x)

f(-1) = ??
f(-1/2) = ??
f(0) = ??
f(1/2) = ??

Answer 8

f(-1)=8?

Answer 9

Very good. What is the area of the 1st rectangle?

Answer 10

8?

Answer 11

Why would that be correct? You have the height, f(-1) = 8. What is the width?

Answer 12

width is 1/2?

Answer 13

so area would be 4? because we are taking 8*1/2

Answer 14

Three more to go!

Answer 15

4,2.5,1,-0.5

Answer 16

YOU GOT IT

Answer 17

is that it? haha

Answer 18

I probably have to add these all together right? and then divide by something?

Answer 19

Please do not divide anything. Just add them. It's not an average. It's a total! It's a Riemann SUM.

Answer 20

duh! I am sorry it is very late where I am haha if I add them all up its gonna be 7

Answer 21

Guess what the RIGHT sum is?

Answer 22

oh dear God!

Answer 23

Then the Midpoint Sum. :-)

No worries. We can get to that when we get to it. Sleep well.

Answer 24

Thank you so much for your help!!