Question

Estimate the area under the curve given the following function, interval, and number of subintervals using the right endpoint method.

f(x) = 1/x; [1,5]; n -4
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Answer 1

To estimate the area under the curve using the right endpoint method, divide the interval [1, 5] into four subintervals of equal width. Evaluate the function 1/x at the right endpoints of these subintervals and multiply the result by the width of each subinterval. Sum up these areas to get an estimate of the total area.

Step-by-step explanation:

To estimate the area under the curve using the right endpoint method, we divide the interval [1, 5] into four subintervals of equal width. The width of each subinterval is given by (b - a) / n, where b is the upper limit of the interval, a is the lower limit of the interval, and n is the number of subintervals.

In this case, b = 5, a = 1, and n = 4. So the width of each subinterval is (5 - 1) / 4 = 1. The right endpoints of the subintervals are 2, 3, 4, and 5.

Now, we evaluate the function 1/x at each of these right endpoints and multiply the result by the width of the subinterval. Finally, we sum up these areas to get an estimate of the total area under the curve.

Using the right endpoint method, the area under the curve of the function f(x) = 1/x over the interval [1, 5] with 4 subintervals is approximately 2.25.