Question
Use the data below to calculate a right hand sum with 5 rectangles to approximate the area under
.
Ask by Wheeler Peters. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To approximate the area under
using a right-hand sum with 5 rectangles, you need the interval
and the function
. First, calculate the width of each rectangle as
. Then, evaluate
at the right endpoints of each subinterval and multiply by
for each rectangle. Sum these values to get the right-hand sum
.
Solution
To calculate the right-hand sum (RHS) with 5 rectangles to approximate the area under the curve
, we need the following information:
- The interval over which we are calculating the area (e.g., from
to ). - The function
. - The width of each rectangle, which can be calculated as
, where is the number of rectangles (in this case, 5). - The heights of the rectangles, which are determined by evaluating the function at the right endpoints of each subinterval.
Please provide the interval
and the function
so that we can proceed with the calculation.
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Beyond the Answer
To calculate the right hand sum with 5 rectangles, we first need to establish the width of each rectangle and the value of the function at the right endpoints. Assume we have an interval
that we are integrating over and that we divide this interval into 5 equal parts, giving us a width
.
Next, we evaluate the function
at the right endpoints of these sub-intervals, namely:
The approximation of the area under the curve using the right-hand sum can then be calculated using the formula:
You can plug in the specific function values for these endpoints to compute the final area approximation.