Using the Midpoint Rule In Exercises 15-20, use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f and the x-axis over the interval. Sketch the region. See Examples 2 and 3.
Function | Interval |
To calculate: The area bounded by the function
Given Information:
The provided function is
Formula used:
The approximate area of any definite integral
Step1: firstly, divide the provided interval of the function into n sub intervals by the use of formula;
Step2: by the use of above calculated value of subinterval find the midpoint of each sub interval.
Step3: final step is to obtain approximate area by calculating function f at each mid-point from the use of formula;
Calculation:
Consider the provided function;
Now, put n equal to 4,
Width
So, the interval
Now, the value of midpoint of each sub interval is calculated as;
For subinterval
For subinterval
For subinterval
So, the mid points of sub intervals are
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