Calculating Lower Sum for f(x) = x^2 +1 between 0 and 2 with Change in X = 1/2

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In summary, the lower sum is used to estimate the area under the curve for a given function. It is calculated by dividing the interval into smaller subintervals and multiplying the value of the function at the left endpoint by the length of each subinterval. A smaller change in x leads to a more accurate estimate, but also requires more calculations. The lower sum is an estimation and cannot give an exact value, but it gets closer as the change in x decreases. Potential sources of error include using a large change in x, using a function that is not continuous or has sharp corners, and human error in calculations.
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Find lower sum...please help!

Homework Statement


Find the lower sum for f(x) = x^2 +1 between 0 and 2 using a change in X = 1/2


Homework Equations





The Attempt at a Solution


[(0^2 + 1) * 1/2] + [(1/2^2 + 1) * 1/2] + [(1^2 + 1) * 1/2] + [(3/2^2 + 1) * 1/2] = 3.75

Is this right?
 
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  • #2
Seems ok to me.
 
  • #3
It would be better to use parentheses for things like (3/2)^2= 9/4 (not 3/2^2= 3/4) but, in fact, you've done that exactly right.
 
  • #4
Thank you! Is there a way to check this on my calculator?
 

Related to Calculating Lower Sum for f(x) = x^2 +1 between 0 and 2 with Change in X = 1/2

1. What is the purpose of calculating the lower sum for a given function?

The lower sum for a function is used to estimate the area under the curve between two given points. This can be helpful in understanding the behavior and properties of the function.

2. How is the lower sum calculated for a function?

The lower sum is calculated by dividing the interval between the two given points into smaller subintervals, with the length of each subinterval determined by the change in x. The value of the function at the left endpoint of each subinterval is then multiplied by the length of the subinterval and all of these values are added together to get the lower sum.

3. What is the significance of using a change in x of 1/2?

The change in x, also known as the width of the subintervals, affects the accuracy of the lower sum. A smaller change in x (i.e. using 1/2 instead of 1) will result in a more accurate estimate of the area under the curve. However, it will also require more calculations and may be more time consuming.

4. Can the lower sum be used to find the exact area under a curve?

No, the lower sum is an estimation and will not give an exact value for the area under a curve. However, as the change in x gets smaller, the lower sum will get closer to the actual area under the curve. To find the exact area, integration techniques must be used.

5. What are some potential sources of error when calculating the lower sum?

Some potential sources of error when calculating the lower sum include using a large change in x, which can result in a less accurate estimate, and using a function that is not continuous or has sharp corners, which may not be well-represented by the subintervals. Additionally, human error in calculations or rounding can also contribute to errors in the final result.

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