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Approximate the area of the region between the graph of the function g(x) = 49x - x³ and the x-axis on the interval [0, 7]. Use n = 4 subintervals, and use the right endpoint of each subinterval when approximating the area for each subinterval. If necessary, round any intermediate calculations to no less than six decimal places and round your final answer to four decimal places.

Approximate the area of the region between the graph of the function g(x) = 49x - x³ and the x-axis on the interval [0, 7]. Use n = 4 subintervals, and use the right endpoint of each subinterval when approximating the area for each subinterval. If necessary, round any intermediate calculations to no less than six decimal places and round your final answer to four decimal places.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Approximate the area of the region between the graph of the function g(x) = 49x - x³ and the x-axis on the interval [0, 7]. Use n = 4 subintervals, and use the right endpoint of each subinterval when approximating the area for each subinterval. If necessary, round any intermediate calculations to no less than six decimal places and round your final answer to four decimal places.
Transcribed Image Text:Approximate the area of the region between the graph of the function g(x) = 49x - x³ and the x-axis on the interval [0, 7]. Use n = 4 subintervals, and use the right endpoint of each subinterval when approximating the area for each subinterval. If necessary, round any intermediate calculations to no less than six decimal places and round your final answer to four decimal places.
Expert Solution
Step 1

Introduction:

First, determine the width x, of each rectangle required for the Riemann sum. The width of each rectangle is the same because we are working with uniform divisions. With respect to n subintervals (or rectangles), ∆x=b-an, where a denotes the definite integral's lower bound and b denotes it's upper bound.

Step 2: Determine where each rectangle's right endpoint is. We call these endpoints x I and we may determine the correct endpoints by solving for xi using the formula xi=a+∆x.i.

Step 3: Determine the appropriate Riemann sum.

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