To use the left-hand rectangular approximation method (LRAM), we divide the interval from x = 0 to x = 12 into four equal subintervals. The width of each subinterval will be 12/4 = 3.
To find the height of each rectangle, we evaluate the function y = x^3 at the left endpoint of each subinterval.
For the first rectangle, when x = 0, y = 0^3 = 0.
For the second rectangle, when x = 3, y = (3)^3 = 27.
For the third rectangle, when x = 6, y = (6)^3 = 216.
For the fourth rectangle, when x = 9, y = (9)^3 = 729.
Now we can find the area of each rectangle:
First rectangle: width = 3, height = 0, so area = 3*0 = 0.
Second rectangle: width = 3, height = 27, so area = 3*27 = 81.
Third rectangle: width = 3, height = 216, so area = 3*216 = 648.
Fourth rectangle: width = 3, height = 729, so area = 3*729 = 2187.
To find the approximate area under the curve, we sum up the areas of the rectangles:
0 + 81 + 648 + 2187 = 2916.
Therefore, the approximate area under the curve from x = 0 to x = 12, using the left-hand rectangular approximation method, is 2,916.
Four rectangles are used to estimate the area under the curve, y=x3 , from x = 0 to x = 12. Using the left-hand rectangular approximation method (LRAM), what is the approximate area under the curve for the given interval? (1 point) Responses 972 972 2,700 2,700 2,916 2,916 5,022 5,022 8,100
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