Calculus

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

asked by Mia
  1. n
    ∑(pi/n)(cos(pi/n)
    t=1

    corrected

    posted by Mia
  2. 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.

    posted by Steve
  3. n
    ∑(pi/2n)(cos(t*pi/2n)
    t=1

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

    posted by Mia
  5. 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!!!

    posted by Steve

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