Question

Write a formula for a Riemann sum for the function f (x )equals 1089 minus x squared over the interval ​[0,33​].

Answer 1

A Riemann sum is a method for approximating the area under a curve by dividing the interval into smaller subintervals and summing up the areas of rectangles.

Step-by-step explanation:

A Riemann sum is a method for approximating the area under a curve by dividing the interval into smaller subintervals and summing up the areas of rectangles. To find the Riemann sum for the function f(x) = 1089 - x^2 over the interval [0, 33], you can use the formula:

Riemann sum = ∑(f(xi) * Δx), where f(xi) is the value of the function at each subinterval, and Δx is the width of each subinterval.

For this particular function and interval, you would divide the interval [0, 33] into n subintervals of equal width, calculate the value of f(xi) for each subinterval, multiply it by Δx, and finally sum up all the results to get the Riemann sum.

Answer 2

Area of 23958

Step-by-step explanation:

The Riemann sum is just the divide of a area into smaller areas and computing the sum of those areas. It is basically the integral of a function over an interval.

`\int\limits {1089-x^2} \, dx`

over the interval [0,33].

`\int\limits {1089-x^2} \, dx=1089x-(x^3)/3`

evaluate

`=0-1089\cdot{33}-(33^3)/3=35937-11979=23958`