Thread: integrals 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.

Originally Posted by memena

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

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,

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

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!

Originally Posted by memena

ok do i draw this graph Mr F says: Yes, use a graphics calculator.

and then add the rectangles, Mr F says: Yes, add the area of each of the four rectangles. As has already been stated, the total area is , where and .

if so can u tell me what it is supposed to look like, Mr F says: Draw the graph (use a graphics calculator to get it) and draw in the rectangles. Then you'll know what it looks like.

im sorry i am completely lost, i don't understand anything! Mr F says: But you must surely have some examples to follow ....?

..

Originally Posted by memena

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!

yes, you can draw a diagram to visualize it.

here:

basically, your finding the area of the 4 rectangles we have in the diagram, that is, length times width for each. the height of each rectangle is given by , the widths are all one