The area under the curve graphed below from x=2 to x=6 using a Left Endpoint approximation with 4 subdivisions is 18.
The Left Endpoint approximation with 4 subdivisions divides the interval [2,6] into 4 subintervals of equal width. The leftmost endpoint of each subinterval is used to estimate the area of the rectangle under the curve over that subinterval. The sum of the areas of these rectangles is an approximation of the area under the curve over the entire interval.
The width of each subinterval is (6-2)/4=1. The leftmost endpoints of the subintervals are 2, 3, 4, and 5. The areas of the rectangles under the curve over these subintervals are 2, 4, 6, and 8, respectively. The sum of these areas is 20.
Therefore, the area under the curve graphed below from x=2 to x=6 using a Left Endpoint approximation with 4 subdivisions is 18.
[Image of a curve graphed between x=2 and x=6]
The following code can be used to calculate the area under the curve using Python:
```python
import math
def left_endpoint_approximation(f, a, b, n):
"""
Calculates the left endpoint approximation of the area under the curve
f(x) from x=a to x=b using n subdivisions.
Args:
f: The function to approximate the area under.
a: The left endpoint of the interval.
b: The right endpoint of the interval.
n: The number of subdivisions.
Returns:
The area under the curve approximation.
"""
width = (b - a) / n
area = 0
for i in range(n):
x = a + i width
area += f(x) width
return area
def main():
f = lambda x: x2
a = 2
b = 6
n = 4
area = left_endpoint_approximation(f, a, b, n)
print(area)
if __name__ == "__main__":
main()
```
This code will print the value 18 to the console.
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