a) Estimate the area under the graph of f(x)=7+4x^2 from x=-1 to x=2 using three rectangles and right endpoints.
R3= ????
Then improve your estimate by using six rectangles.
R6= ?????
Sketch the curve and the approximating rectangles for R3.
Sketch the curve and the approximating for R6.
b) Repeat part (a) using left endpoints.
L3= ???
L6= ????
Sketch the curves and the approximating rectangles for L3 and L6.
c) Repeat part (a) using midpoint.
M3 =???
M6= ???
Sketch the curves and the approximating rectangles for M3 and M6.
d) From your sketches in parts (a)-(c) which appears to be the best estimate?
R6
M6
or
L6
I know this is a lot but I didn't understand this topic and I have several questions like this. If you do this for me that way I can do the rest of my HW.
Thank you so much!!!!
2 answers
x = -1 to x = 2
take a look at this article:
http://mathworld.wolfram.com/RiemannSum.html
you can estimate the true area under the curve by drawing rectangles under the curve and adding up their areas.
But, wince the rectangles have flat tops, they don't really fit the curve. So, pick either the left side or the right side to estimate the curve's height. The rectangles will be completely under the curve, or will stick out above it a bit.
With that in mind, take a stab at it.
The three rectangles in the interval [-1,2] will require four points on the curve, at
x y
-1 11
0 7
1 11
2 23
http://mathworld.wolfram.com/RiemannSum.html
you can estimate the true area under the curve by drawing rectangles under the curve and adding up their areas.
But, wince the rectangles have flat tops, they don't really fit the curve. So, pick either the left side or the right side to estimate the curve's height. The rectangles will be completely under the curve, or will stick out above it a bit.
With that in mind, take a stab at it.
The three rectangles in the interval [-1,2] will require four points on the curve, at
x y
-1 11
0 7
1 11
2 23
1 answer