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Let f(1) be the rate of flow, in cubic meters per hour, of a flooding river at time t in hours. Give an integral for the total flow of the river. (a) Over the time period 0

Let f(1) be the rate of flow, in cubic meters per hour, of a flooding river at time t in hours. Give an integral for the total flow of the river. (a) Over the time period 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let f(1) be the rate of flow, in cubic meters per hour, of a flooding river at time t in hours. Give an integral for the total flow of the river. (a) Over the time period 0 <t< 120. 120 Total flow = f(t) dt cubic meters. 120 f(t) dt cubic meters. Total flow = t 120 Total flow = I f'(1) dt cubic meters. 120 Total flow = | tf' (1) dt cubic meters. 120 Total flow tf(t) dt cubic meters. (b) In terms of T in days, for the same time interval. Total flow = f(24T) dT cubic meters. Total flow f(T) dT cubic meters. 5 Total flow f(24T)24 dT cubic meters. Total flow | f'(24T)24 dT cubic meters. Total flow | f(24T)24T dT cubic meters.
Transcribed Image Text:Let f(1) be the rate of flow, in cubic meters per hour, of a flooding river at time t in hours. Give an integral for the total flow of the river. (a) Over the time period 0 <t< 120. 120 Total flow = f(t) dt cubic meters. 120 f(t) dt cubic meters. Total flow = t 120 Total flow = I f'(1) dt cubic meters. 120 Total flow = | tf' (1) dt cubic meters. 120 Total flow tf(t) dt cubic meters. (b) In terms of T in days, for the same time interval. Total flow = f(24T) dT cubic meters. Total flow f(T) dT cubic meters. 5 Total flow f(24T)24 dT cubic meters. Total flow | f'(24T)24 dT cubic meters. Total flow | f(24T)24T dT cubic meters.
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