Calculus on Demand at Dartmouth College Lecture 25 | Index | Lecture 27 Lecture 26 ## Resources

Math 3 Course Syllabus
Practice Exams

# Contents

In this lecture we consider a real-world application of modeling with accumulations by developing a case study on river flooding. This material is the extended application and culmination of our work in lectures 21-26.

### Quick Question

What is the approximate area under the graph of the function 1/(1 + x) on the interval [0,1] using the two inscribed rectangles on the intervals [0,1/3] and [1/3,3/4]? (You need not simplify your answer.) ### Outline

Outline for Case Study: Flood Watch

### Textbook

Case Study: Flood Watch

### Quiz

Case Study: Flood Watch Quiz

### Examples

• Calculate the centroid of the region between the curves f(x) = x2 + 2 and g(x) = 2x + 5 for x in the interval [–1, 3].
• A certain river has rainfall discharge data and rainfall recorded during and after a storm. Find the base flow of the river, the total volume of rainfall discharge, and the lag time between the rainfall event and the rainfall discharge.
• A flower grows at varying rates, measured at the beginning of each month and halfway through each month, according to a chart. What is the approximate height of the flower after three months? Consider a second flower that requires fertilizer to grow, and compute the lag time between the application of fertilizer and the flower's growth.

### Videos

Lecture 25 | Index | Lecture 27