Respuesta :
To use upper and lower sums to approximate the area of the region under the curve y = √6x, we need to divide the interval of integration into a certain number of subintervals of equal width.
Let's say that we want to divide the interval [a, b] into n subintervals of equal width. We can then define the points x0, x1, ..., xn as follows:
x0 = a
x1 = a + (b - a)/n
x2 = a + 2(b - a)/n
...
xn = b
The width of each subinterval is (b - a)/n.
We can then use these points to define the upper sum and lower sum as follows:
Upper sum = ∑ (b - a)/n * max(f(x))
Lower sum = ∑ (b - a)/n * min(f(x))
where the sum is taken over all subintervals, and max(f(x)) and min(f(x)) represent the maximum and minimum values of the function f(x) on each subinterval, respectively.
To calculate the upper and lower sums, we need to evaluate the function f(x) at each of the points x0, x1, ..., xn. For example, if we want to calculate the upper sum using 4 subintervals, we would evaluate the function at the points x0, x1, x2, and x3, and then use these values to calculate the upper sum using the formula above.
Once we have calculated the upper and lower sums, we can use them to approximate the area of the region under the curve. The area of the region is approximately equal to the average of the upper and lower sums.
For example, if the upper sum is 1.5 and the lower sum is 0.5, then the area of the region is approximately (1.5 + 0.5)/2 = 1.
In general, as we increase the number of subintervals, the upper and lower sums will get closer and closer to the actual area of the region, and the approximation will become more accurate.
Learn more about Area at:
brainly.com/question/25292087
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