An Area Problem;A Speed-Distance Problem v=f(x 2 6 Figure 5.1.1 Main Meny cmew59时
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. An Area Problem; A Speed-Distance Problem
y本 212223 2, a=x0 x1 x2 X3 xn=b Figure 5.1.2 Main Meny C 007e
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved
An Area Problem;A Speed-Distance Problem Figure 5.1.3 (5.1.1) m1△x1+m2△x2+·+mn△xn≤area of2, Main Meny☐ own6
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. An Area Problem; A Speed-Distance Problem
5.12） area of2≤M△r1+M△x2+…+Mn△xn. Main Meny 5
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved
An Area Problem;A Speed-Distance Problem A sum of the form m1△x1+m2△x2+···+m,△xn is called a lower sum for f. area of shaded region is a lower sum for f Figure 5.1.4 Main Meny C
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. An Area Problem; A Speed-Distance Problem A sum of the form m1Δx1 + m2Δx2 +· · ·+mnΔxn is called a lower sum for f
A sum of the form M1△x1+M2△x2+··+Mn△xn is called an upper sum for f. area of shaded region is an upper sum forf Figure 5.1.5 Main Meny own6
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. A sum of the form M1Δx1 + M2 Δx2 +· · ·+ Mn Δxn is called an upper sum for f
An Area Problem:A Speed-Distance Problem If an object moves at a constant speed for a given period oftime,then the total distance traveled is given by the familiar formula distance speed x time. Main Menu cmew59时
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. An Area Problem; A Speed-Distance Problem If an object moves at a constant speed for a given period of time, then the total distance traveled is given by the familiar formula distance = speed ×time
The Definite Integral of a Continuous Function (5.2.10 By a partition of the closed interval [a,b],we mean a finite subset of [a,b]which contains the points a and b. Main Meny C 007e
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. The Definite Integral of a Continuous Function
Example 1 The sets{0,1,{0,5,1},{0,4,h,1},{0,4,3,2,58,1} are all partitionsof the interval [0,1]. Main Meny o
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. Example 1 The sets {0, 1}, {0, ½, 1}, {0, ¼, ½, 1}, {0,1/4, 1/3, 1/2, 5/8, 1} are all partitions of the interval [0, 1]
The Definite Integral of a Continuous Function If P=....is a partition of [a,b],then P breaks up [a,] into n subintervals xox1l[x,x3l,.,[,1.x]of lengths△x,△2..，△xr Main Menu 5
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2007 © John Wiley & Sons, Inc. All rights reserved. The Definite Integral of a Continuous Function If P = {x0 , x1 , x2 , . . . , xn−1, xn} is a partition of [a, b], then P breaks up [a, b] into n subintervals [x0 , x1 ], [x1 , x2 ], . . . , [xn−1, xn ] of lengths Δx1 , Δx2 , . . . , Δxn