Using upper and lower sums to approximate the area.

In summary, the conversation discusses using upper and lower sums to approximate the area of a region with a given domain and number of subintervals. The main issue is taking the sum of the square root of the subinterval endpoints, but the suggestion is to focus on finding the area of rectangles with equal widths and varying heights. The advice is to draw sketches for both a lower and upper sum as a visual aid.
  • #1
Phyzwizz
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0
Never Mind

I answered my own question two minutes after posting it. I don't know how to take this question down so I just deleted it.
 
Last edited:
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  • #2
Phyzwizz said:
I was absent the day our class covered these and so I am struggling to figure out to do this problem.

Use upper and lower sums to approximate the area of the region using the indicated number of subintervals (of equal length).
y=√x the domain is [0,1] with 4 sub intervals of 1/4

I tried looking at how the book did the problem but I keep getting stuck in this problem on the part where you have to take the sum of the square root of i. Is there a way around this because I was never taught any sort of equation to use in order to do that.

Forget about i, which is used in more general presentations. Your interval [0, 1] is divided into four equal subintervals, each of length 1/4. For an upper sum or a lower sum, you need to find the area of four rectangles of width 1/4 and height, the square root of one of the subinterval endpoints.

Draw a sketch if you haven't already done so. In fact, draw two sketches, one for your lower sum and one for your upper sum.
 

1. What are upper and lower sums used for in approximating area?

Upper and lower sums are used to estimate the area under a curve or between two curves. This method is commonly used in calculus and helps to visualize and understand the concept of integration.

2. How do you calculate upper and lower sums?

To calculate the upper sum, first divide the area under the curve into equal subintervals. Then, take the maximum value of the function within each subinterval and multiply it by the width of the subinterval. The sum of these values will give you the upper sum. The same process applies for calculating the lower sum, except you use the minimum value of the function within each subinterval.

3. How accurate are upper and lower sums in approximating area?

The accuracy of upper and lower sums depends on the number of subintervals used. The more subintervals, the closer the approximation will be to the actual area. This method becomes more accurate as the width of the subintervals decreases.

4. Can upper and lower sums be used for any type of curve?

Yes, upper and lower sums can be used for any continuous curve. However, the accuracy of the approximation may vary depending on the complexity of the curve.

5. Are there any limitations to using upper and lower sums to approximate area?

One limitation of using upper and lower sums is that it can be time-consuming for more complex curves. Additionally, this method may not provide an exact answer, but rather an estimate. It is important to understand the limitations and use upper and lower sums as a visual aid rather than a precise calculation.

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