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:

Printable View

- 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 $\displaystyle x_i$ for $\displaystyle i = 0,1,2,...$. so we have $\displaystyle x_0 = -1.5, ~x_1 = -0.5, ~x_2 = 0.5, \mbox{ and } x_3 = 1.5$

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

$\displaystyle A = \sum_{i = 0}^3 f(x_i) \Delta x$

where $\displaystyle \Delta x = x_1 - x_0 = x_2 - x_1 = ... = 1$ and of course, $\displaystyle f(x) = e^{-x^2}$ - Jan 21st 2008, 06:36 PMJhevon
to expound:

since $\displaystyle \Delta x = 1$, the area estimate is given by:

$\displaystyle \sum_{i = 0}^3 f(x_i) = f(x_0) + f(x_1) + f(x_2) + f(x_3)$

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