Calculus

posted by .

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!!!!

  • Calculus -

    x = -1 to x = 2

  • Calculus -

    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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Estimate the area under the graph of f(x) = 2x^3 + 3 from x= -1 to x=5, first using 6 approximating rectangle and right endpoints, and then improving your estimate using 12 approximating rectangles and right endpoints. When using the …
  2. Calculus

    Question Details: Do the following. (Round your answers to four decimal places.) (a) Estimate the area under the graph of f(x) = 8 + 2x2 from x = -1 to x = 2 using three rectangles and right end-points. R3 = 1 Improve your estimate …
  3. Math: Calculus

    Estimate the area under the graph of f(x)=3x^3+5 from x=-1 to x=4, first using 5 approximating rectangles and right endpoints, and then improving your estimate using 10 approximating rectangles and right endpoints. I'm having problem …
  4. Math

    Estimate the are under the curve f(x)=x^2-4x+5 on [1,3]. Darw the graph and the midpoint rectangles using 8 partitions. Show how to calculate the estimated area by finding the sum of areas of the rectangles. Find the actual area under …
  5. Math: Need Answer to study for a quizz. Help ASAP

    Estimate the area under the curve f(x)=x^2-4x+5 on [1,3]. Darw the graph and the midpoint rectangles using 8 partitions. Show how to calculate the estimated area by finding the sum of areas of the rectangles. Find the actual area under …
  6. calculus

    4. a. Estimate the area under the graph of f(x)=sqrt(x^2+4) from x=0 to x=2 using four rectangles and right endpoints.
  7. Calculus

    Estimate the area under the graph of 25−x 2 from x = 0 to x = 5 using 5 left rectangles. b. Sketch for yourself the graph of f and the rectangles. Is this left sum an overestimate or underestimate?
  8. Calculus-Approximate areas

    Estimate the area under the graph of f(x)= x^2 + 3 x from x=1 to x=10 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve at a) left endpoints: b) right endpoints:
  9. Calculus Help Please Urgent!!!

    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= ?
  10. Calculus

    Estimate the area under the graph of f(x)=cos((pi/4)x) from x=-2 to x=2 using 3 rectangles of equal width, using left and right endpoints.?

More Similar Questions