The interval [1, 9] is partitioned into n subintervals [xk-1, xk] for k = 1, ..., n, each of width Ax. Choose any such that ¤k-1 ≤ x ≤ xk. Let the function f be continuous over [1,9]. Do the following. ² [₁²₁ (a) State the limit definition of f(x) dx. (b) Estimate the integral in (a) if f(x) = x² using a Riemann sum with n = 4 subintervals of equal width and sample points x k for k= 1, 2, 3, 4. = (c) Sketch f(x) = x² and the rectangles whose area is the Reimann sum in (b). Use this sketch to explain why the sum in (b) overestimates the value of the integral in (a) when f(x) = x².
The interval [1, 9] is partitioned into n subintervals [xk-1, xk] for k = 1, ..., n, each of width Ax. Choose any such that ¤k-1 ≤ x ≤ xk. Let the function f be continuous over [1,9]. Do the following. ² [₁²₁ (a) State the limit definition of f(x) dx. (b) Estimate the integral in (a) if f(x) = x² using a Riemann sum with n = 4 subintervals of equal width and sample points x k for k= 1, 2, 3, 4. = (c) Sketch f(x) = x² and the rectangles whose area is the Reimann sum in (b). Use this sketch to explain why the sum in (b) overestimates the value of the integral in (a) when f(x) = x².
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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