Riemann Sum: Solve for Area Under Curve 0 to 18

In summary, a Riemann sum is a method for estimating the area under a curve by dividing it into smaller rectangles and calculating their areas. To solve for the area, the rectangles are added together. The range in the formula represents the interval of calculation, and Riemann sums can only provide an estimate and have limitations such as accuracy and applicability to continuous functions.
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blahblah33
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Riemann sum help!

Homework Statement


Use Riemann sum with ci= i3/n3
f(x)= [tex]\sqrt[3]{x}[/tex] +12
from x=0 to x=18
n= 6 subintervals
Approximate the sum using Riemann's Sum

Homework Equations


[tex]\Sigma f(ci) \Delta[/tex] xi
is the equation for riemanns sum i think

The Attempt at a Solution


i tried plugging in stuff using that, but i must've done something wrong because the answer i got was 200 off the actual area under the curve...
 
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also, is my original equation for riemann's sum correct? is there a limit involved?
 

Related to Riemann Sum: Solve for Area Under Curve 0 to 18

1. What is a Riemann sum?

A Riemann sum is a method for approximating the area under a curve on a graph. It involves dividing the area into smaller rectangles and calculating the area of each rectangle to get an estimate of the total area.

2. How do you solve for the area under a curve using Riemann sums?

To solve for the area under a curve using Riemann sums, you need to first divide the area into smaller rectangles. Then, calculate the area of each rectangle by multiplying its width by its height. Finally, add up the areas of all the rectangles to get an estimate of the total area.

3. What is the significance of the 0 to 18 range in the Riemann sum formula?

The 0 to 18 range represents the interval over which we are calculating the area under the curve. In this case, it means we are calculating the area under the curve from x = 0 to x = 18.

4. Can Riemann sums be used to find the exact area under a curve?

No, Riemann sums can only provide an estimate of the area under a curve. As the number of rectangles used in the approximation increases, the estimate gets closer to the actual area, but it will never be exact.

5. Are there any limitations to using Riemann sums to approximate the area under a curve?

Yes, there are limitations to using Riemann sums. The accuracy of the estimation depends on the number of rectangles used, so using too few rectangles can result in a less accurate estimate. Additionally, Riemann sums are only applicable for continuous functions, so they cannot be used for discontinuous or undefined functions.

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