Which of the following is a right Riemann sum for ∫831+x−−−−−√ⅆx ?
To find the right Riemann sum for the given integral ∫√(831+x) dx, we first need to understand what a Riemann sum represents
To find the right Riemann sum for the given integral ∫√(831+x) dx, we first need to understand what a Riemann sum represents. A Riemann sum is an approximation of the definite integral of a function over a given interval. It is calculated by dividing the interval into subintervals and then evaluating the function at specific points within each subinterval.
In this case, since we are asked for a right Riemann sum, we need to evaluate the function at the right endpoints of each subinterval.
Let’s denote the subintervals as [a, b], [b, c], [c, d], …, where a, b, c, d, … are the endpoints of the subintervals.
To determine the size of each subinterval, we need to divide the given interval into n equal parts, where n represents the number of subintervals. Thus, the width of each subinterval is Δx = (b – a) / n.
Now, we can define the right Riemann sum formula:
R_n = f(b) Δx + f(c) Δx + f(d) Δx + … + f(j) Δx
Here, f represents the given function, and (b, c, d, …, j) are the right endpoints of the subintervals.
In this case, the given function is f(x) = √(831 + x), and we are not provided with the number of subintervals, n, or the values of a, b, c, d, …, j. This means that we cannot provide a specific right Riemann sum without more information.
However, if we are given the number of subintervals, n, and the endpoints of the interval, we can calculate the right Riemann sum using the formula outlined above.
More Answers:
Calculating the Left Riemann Sum for ∫101f(x)ⅆx using Given TableDetermining the Limit for Definite Integral ∫31sin(x^3+2)dx | Analysis and Evaluation
Finding the Limit of a Summation Expression as n Approaches Infinity: Math Tutorial for Calculating the Value of a Limit