Question

Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 4 of x squared, dx.

Answer 1

https://gyazo.com/fb167f84247cce45c0a7f27ba176a684

Answer 2

@terenzreignz last question of the course

Answer 3

Ugh. And it had to be an extremely tedious one.
All right, get the upper and lower sum estimates.

Answer 4

Good thing the width of each partition is 1. We can do this relatively quickly.

Okay, first up, lower sum.
The intervals are [0,1], [1,2], [2,3], and [3,4]
Lower sum gets the lower ends of each interval.

0,1,2, and 3.
Evaluate the function at all these points.

Answer 5

How would that be done?

Answer 6

Ok

Answer 7

14?

Answer 8

Good ^^
Now upper sum.
Get the higher end of the intervals.
1,2,3, and 4
And evaluate at those points.

Answer 9

30

Answer 10

Now trapezoidal?

Answer 11

Okay.
Now evaluate the integral using the trapezoidal rule :)

Answer 12

That's not right, I got 8.

Answer 13

I see what I did.

Answer 14

Got 22

Answer 15

Which is right :)

Answer 16

Good ^^
Indeed, that is the average of 14 and 30

Answer 17

14+30=44

Answer 18

/2=22

Answer 19

Well done ^^

Answer 20

8/8 m8 you've been gr8 hope u know i appreci8 that u were nvr l8 to our d8 :)

Answer 21

what is with your obsession with 8?

Answer 22

Lol

Answer 23

the ryhmes what else?

Answer 24

It's just something done online as a joke (basically mocking brits)

Answer 25

Okay then :)
I'll be seeing you, maybe.

Signing off ^^