To estimate the area using the right-hand rectangular approximation method (RRAM), we divide the interval [0, 6] into three equal-sized subintervals of width 2.
The height of each rectangle is determined by the right endpoint of each subinterval.
For the first subinterval [0, 2], the right endpoint is x = 2.
Using this value in the equation y = x^2 + 4, we get y = 2^2 + 4 = 8.
So, the height of the first rectangle is 8.
For the second subinterval [2, 4], the right endpoint is x = 4.
Using this value in the equation y = x^2 + 4, we get y = 4^2 + 4 = 20.
So, the height of the second rectangle is 20.
For the third subinterval [4, 6], the right endpoint is x = 6.
Using this value in the equation y = x^2 + 4, we get y = 6^2 + 4 = 40.
So, the height of the third rectangle is 40.
The width of each rectangle is 2 (the width of each subinterval).
Therefore, the area of each rectangle is the product of its width and height:
Area of first rectangle = 2 * 8 = 16
Area of second rectangle = 2 * 20 = 40
Area of third rectangle = 2 * 40 = 80
The approximate area under the curve using RRAM is the sum of the areas of the three rectangles:
16 + 40 + 80 = 136
So, the approximate area under the curve for the given interval is 136.
Three rectangles are used to estimate the area under the curve, y=x2+4 , from x = 0 to x = 6. Using the right-hand rectangular approximation method (RRAM), what is the approximate area under the curve for the given interval? (1 point) Responses 47 47 64 64 68 68 94 94 136
1 answer
1 answer