Chapter 7 Integral Calculus 積分

重點 1.The antiderivative F(x) of a function f(x) is the function such that: 一函數 f(x) 之反微分 F(x) 為一符合下式之函數 :

2.An indefinite integral is the same thing as the antiderivative function. 不確定積分與反微分同義

瑕積分

7.1 The Antiderivative of a Function 函數的反微分 位置 (position) 、速度 (velocity) 、 加速度 (acceleration) 速度是位置對時間的微分 (velocity is the derivative of the position with respect to time) 加速度是速度對時間的微分 (acceleration is the derivative of the velocity with respect to time)

(7.1) (7.2) (7.3)

EXAMPLE 7.1(a) The downward gravitational acceleration is equal to a z = -g, the velocity and position are:

Rules about Integrals ( 積分規則 ) 7.2 The Process of Integration Figure 7.4

Figure 7.5

Exercise 7.8, Chapter 7 (a=1)

p. 78: a. The product of two even functions is an even function. b. The product of two odd functions is an even function. c. The product of an odd function and an even function is an odd function.

What do these numbers mean?

7.3 Tables of Indefinite Integrals 不定積分表

7.4 Improper Integrals 瑕積分

7.5 Techniques of Integration

作業 15: Exercise 7.12

Example 7.12 Apply Eq. (7.45) to

Example 7.14 Consider a chemical reaction where the capital letters are abbreviations for some chemical formulas and the lowercase letters are abbreviations for the stoichiometric coe- fficients that balance the equation. Assume that the rate of the reaction is given by the rate law where is a function of temperature called the rate constant and where represents the molar concentration of A and represents the molar concentration of B. This rate law is said to be second order overall, first order in A, and first order in B. Carry out the integration of this rate law using the method of partial fractions.

7.6 Numerical Integration 數值積分 ( 略 )