By using finite approximation to estimate the area under the graph of the function using a lower sum with two rectangles of equal width of the function f(x)=x^2 in the interval [0,1] will be?
- 0.125
- 0.2187
- 0.625
- None of these
Explanation
To estimate the area under the graph of f(x) = x^2 in the interval [0,1] using a lower sum with two rectangles of equal width:
Width of each rectangle = (1 - 0) / 2 = 0.5
Rectangle 1: Height = f(0) = 0^2 = 0, Area = 0 * 0.5 = 0
Rectangle 2: Height = f(0.5) = 0.5^2 = 0.25, Area = 0.25 * 0.5 = 0.125
Total estimated area = 0 + 0.125 = 0.125
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