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1、Chapter 4 Integration,4.3 Estimating with Finite Sums,4.1 Indefinite Integrals,Differential Equations,and Modeling,4.2 Integral Rules,Integration by Substitution,4.4 Riemann Sums and Definite Integrals,4.5 The Mean Value and Fundamental Theorems,4.6 Substitution in Definite Integrals,4.7 Numerical I
2、ntegration,4.6,Substitution in Definite Integrals,4.6.1 Substitution in Definite Integral,4.6.2 Area between Curves,Solution 1.,Solution 2.,Example.Evaluate the integrals,Solution.,Example.Evaluate the integrals,Solution.,4.6.2,Area between Curves(曲线之间的平面图形面积),Step 1.Subdivide the interval a,b into
3、subintervals.,Step 2.Select some number in each subinterval,and then obtain many rectangles.,Step 3.Take the sum of above products.,Step 4.Take the limitation of Riemann sum.,Notice that both f and g are continuous.Therefore,we have,Solution.,Solution 1.,Solution 2.,Does it has other Solutions?,Example.Evaluate the area of the shade region.,Example.Evaluate the area of the shade region.,Example.Evaluate the area of the shade region.,Example.Evaluate the area of the shade region.,Example.Evaluate the area of the shade region.,Exercises,P371 1(a),4(a),5(a),6(a),8(a),12,15.P372 19,24.,
