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The area of the region under the graph of f(x)=4 + 1x over the closed interval 0≤ x ≤ 1 by choosing representative point as the right endpoint of each subinterval is given by
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The approximate value of the area between the graph of f(x) = 2x2 + 1 and the interval (0,2) by choosing n = 5 rectangles is given by
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The area of the region under the graph of f(x)=4 + 1x over the closed interval 0≤ x ≤ 1 by choosing representative point as the right endpoint of each subinterval is given by
You don't specify the width of the sub-interval, but we can choose a convenient value, say, .25
The area in this case is the sum of [ the rectangle widths * their heights ].....because we are using the right endpoints, the area will be over-stated
.25 (4 + .25) + .25 ( 4 + .50) + .25 + .25 ( 4 + .75) + .25 ( 4 + 1) =
.25 [ 4.25 + 4.5 + 4.75 + 5 ] = 4.625
BTW....the TRUE area is given by ( 4 ( 1) + (1/2) ) = 4.5
If we made the widths of thes sub-intervals smaller, we would get a better approximation ....
