Calculus Volume 2 · 免费预览
积分的其他策略
除核心技巧之外，积分还考验代数准备、巧妙代换、积分表的运用以及计算机代数；而真正需要掌握的是对各种方法何时适用的整体判断。
1. The strategic overview
The strategic overview
2. Algebraic preprocessing
Algebraic preprocessing
3. Integral tables and computer algebra
Integral tables and computer algebra
4. When no elementary antiderivative exists
When no elementary antiderivative exists
5. Diagnostic order
An integrand is a rational function, a ratio of polynomials. Which technique is designed for it?
6. Preprocessing example
Which algebraic step unlocks the integral of (x^2 + 1)/x dx?
7. Nonelementary integral
Which integral has no elementary antiderivative?
8. Rationalizing substitution
The integral of dx/(1 + sqrt(x)) is unlocked by which substitution?
9. Clever multiplication
The trick for integrating sec x multiplies by (sec x + tan x) over itself. What does this manufacture?
10. Integral table role
Before computer algebra, working integrators consulted printed collections of standard antiderivatives. As two words, what were these called? Answer like answer keys.
11. Why learn techniques with CAS
Computer algebra systems integrate instantly. Why does the course still teach the manual techniques?
12. Error function domain
The error function erf(x) is defined by an integral of e^(-t^2). Since no elementary antiderivative exists, erf is an example of what kind of function? Answer with two words.
13. CAS expansion
Computer algebra systems apply the full integration decision procedure automatically. As a three-letter abbreviation, what are these systems called? Answer in lowercase.
14. Diagnostic first try
In the diagnostic order, the first technique to try for an unfamiliar integrand is which one, named after the chain rule's reversal? Answer with one word.