Calculus

posted by Mia

Determine an upper/lower estimate for the area under the curve f(x) = cos x between x = 0 and x = pi/2 . Show how you arrive at this estimate.

This is the question that my teacher wanted us to answer and I'm not sure how to even start the process.

Should I use Reimann's Sum? If so how do I do it?

n
∑(pi/n) (cos(ipi/2n)

Also, wondering if this is a start?
t=1

  1. Mia

    n
    ∑(pi/n)(cos(pi/n)
    t=1

    corrected

  2. Steve

    It's a good start. Note that since you are using the right-side sum, and cos(x) is concave down and rising on that interval, the sum will be an upper estimate.

    Use the left-side sum for a lower estimate.

    Draw a few rectangles and the curve to see why this is true.

  3. Steve

    n
    ∑(pi/2n)(cos(t*pi/2n)
    t=1

  4. Mia

    Okay I'm just confused about how many rectangles to use? Also, if I should only worry about [0,pi/2]

  5. Steve

    Use as many as you want. That's the n.

    You can estimate the area with a single rectangle, of width pi/2 and height 1, but it won't be a very good estimate.

    Also, my bad. I was thinking of sin(x) when I mentioned that the estimate was over- or under-. The reverse for cos(x), since it is decreasing on the interval.

    And yes, you need to worry about the interval, since that was what was specified in the problem!!!

Respond to this Question

First Name

Your Answer

Similar Questions

  1. CALC

    Let f(x) be the function e^sin(x/10). If you wanted to estimate the area under the curve for this function from 3 to 5, how many intervals would you need to use to be sure that your upper and lower bounds differered by no more than …
  2. Calculus

    t 2 4 6 8 10 12 v(t) 44 42 41 40 37 35 the velocity in the table is decreasing 2 </= x </= 12. Using n=5 subdivisions, approximate the total distance traveled for: a) an upper estimate b) a lower estimate i'm not quite sure what …
  3. calc

    t 2 4 6 8 10 12 v(t) 44 42 41 40 37 35 the velocity in the table is decreasing 2 </= x </= 12. Using n=5 subdivisions, approximate the total distance traveled for: a) an upper estimate b) a lower estimate i'm not quite sure what …
  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

    Estimate the area under the curve f(x)=x^2 between x=0 and x=1 using 4 rectangles of equal width if a) The height is taken from the right endpoint b) The height is taken from the midpoint. I have no idea what exactly this question …
  7. Math

    1.) Your velocity is given by v(t) = t^2 + 6 in m/sec, with t in seconds. Estimate the distance, S, traveled between t= 0 and t = 5. Use an overestimate with data every one second. The distance is approximately ___________ m. Please …
  8. Python programming

    A standard problem in mathematics is to measure the area under a curve (or to integrate the function defining the curve). A simple way to do this is to approximate the area with a series of rectangles (whose areas are easy to compute). …
  9. Calculus

    Estimate the area under the curve f(x) = x2 + 1 from x = 0 to x = 6 by using three circumscribed (over the curve) rectangles. Answer to the nearest integer.
  10. calculus

    Estimate the area under the curve f(x) = x2 from x = 1 to x = 5 by using four inscribed (under the curve) rectangles. Answer to the nearest integer.

More Similar Questions