Write and evaluate a sum to approximate the area under y = (x – 4)2 – 1 for the domain 0 ≤ x ≤ 2.
a. Use inscribed rectangles 0.5 units wide.
b. Use circumscribed rectangles 0.5 units wide.

Question

Write and evaluate a sum to approximate the area under y = (x – 4)2 – 1 for the domain 0 ≤ x ≤ 2.
a. Use inscribed rectangles 0.5 units wide.
b. Use circumscribed rectangles 0.5 units wide.

terenzreignz · Answer

What's inscribed and circumscribed?

anonymous · Answer

are you asking me or dont ya know?

terenzreignz · Answer

I don't know :D
I have an idea how to do this, but I can't guarantee any output from myself without knowing what in the blazes inscribed and circumscribed mean :D

anonymous · Answer

oh haha, okay, well thats why i need help, im not quite sure myself

terenzreignz · Answer

Okay, I got it :)
But first, let's draw that pretty little graph...
|dw:1363961528489:dw|

terenzreignz · Answer

y = 2x - 9|dw:1363961611966:dw|

terenzreignz · Answer

Actually, let's zoom in...
|dw:1363961680184:dw|Something like that, i reckon :D

anonymous · Answer

ok :)

terenzreignz · Answer

So, if x goes from 0 to 2, it's approximately this region right here...|dw:1363961794958:dw|(openstudy draw should have a fill tool :D )

terenzreignz · Answer

Anyway, It's tricky illustrating inscribed and circumscribed rectangles in this example, so let's look at a new one...
|dw:1363961924927:dw|say we divide this part into rectangular regions, like so...

terenzreignz · Answer

First, divide into intervals...|dw:1363961981592:dw|

terenzreignz · Answer

The inscribed rectangles are the ones still inside the region...|dw:1363962023629:dw|
while the circumscribed rectangles are the ones that sort of exceed it, ie, go outside, like...|dw:1363962110435:dw|
Sorry for the bad drawings :)