Question

Let rn denote the right-endpoint sum using n subintervals. Compute the indicated right sum for the given function on the indicated interval. (Round your answer to four decimal places.) r6 for f(x) = 1 x(x - 1) on [4, 7]

Answer 1

The right-endpoint sum is a method to approximate the area under a curve using right endpoints of subintervals. To compute the indicated right sum, we divide the interval [4, 7] into 6 subintervals and find the width of each subinterval, Δx. We then evaluate the function at each right endpoint and multiply it by the height of the function at that endpoint.

Step-by-step explanation:

The right-endpoint sum is a method to approximate the area under a curve using right endpoints of subintervals. To compute the indicated right sum, we need to divide the interval [4, 7] into n subintervals and find the width of each subinterval, Δx. In this case, n = 6, so Δx = (7 - 4) / 6 = 0.5.

Next, we evaluate the function at each right endpoint. For each subinterval, we take the right endpoint value and multiply it by the height of the function at that endpoint. In this case, the function is f(x) = 1 / (x(x - 1)). So, we have:

• For the first subinterval, x = 4 + 0.5 = 4.5. f(4.5) = 1 / (4.5 * (4.5 - 1)).
• For the second subinterval, x = 4.5 + 0.5 = 5.5. f(5.5) = 1 / (5.5 * (5.5 - 1)).
• And so on for the remaining subintervals.

Finally, we sum up all the individual areas to find the approximation of the total area under the curve. Round the answer to four decimal places.