Chapter 4: Integration
Section 4.1 - Area by Riemann Sums
Section 4.2 - The Definite Integral
Section 4.3 - Fundamental Theorem of Calculus and the Indefinite Integral
Section 4.4 - Integration by Substitution
Section 4.5 - Improper Integrals
Section 4.6 - Average Value and the Mean Value Theorem
Integral calculus stems from the question "How can area under a curve be computed?" Amazingly enough, the answer to this question is related to the answer to the question about curves having slope. Indeed, the area under a curve can be found as the limiting value of the sum of small bits of area, and this summative process reduces to finding an antiderivative of the curve under which the area is to be computed. In other words, if the expression for the area is given by F, then the curve for which it gives the area is F′. Why all this should be so is the content of Chapter 4.
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