Estimate the area under the graph of f(x) = e^-x^2 from x = -2 to x = 2 using four approximating rectangles and midpoints.

(Doh):confused:

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- Jan 21st 2008, 06:11 PMmemenaintegrals pls help asap
Estimate the area under the graph of f(x) = e^-x^2 from x = -2 to x = 2 using four approximating rectangles and midpoints.

(Doh):confused: - Jan 21st 2008, 06:18 PMJhevon
divide the interval [-2,2] into four equal sub-intervals. that is, we partition it into the intervals: [-2,-1], [-1,0], [0,1] and [1,2]

now, take the midpoints of these rectangles, and label them by for . so we have

now we can use a finite Riemann sum to estimate the area. thus, an estimate of the area is given by:

where and of course, - Jan 21st 2008, 06:36 PMJhevon
to expound:

since , the area estimate is given by:

now i hope you can continue from there

if you are not clear on something, say so - Jan 21st 2008, 07:02 PMmemenaummm
ok do i draw this graph and then add the rectangles, if so can u tell me what it is supposed to look like, im sorry i am completely lost, i don't understand anything!(Speechless)

- Jan 21st 2008, 07:12 PMmr fantastic
- Jan 21st 2008, 07:14 PMJhevon