Calculus 2 Connections Map

Calculus 2 · Axiom Academy

SUMMARY Calculus 2 Connections Map The whole course on one page — five big topics and the single thread, the integral as an infinite sum, that ties them together. Calculus 2 is one idea wearing five hats: add up infinitely many infinitesimal pieces . Integrals, series, arc lengths, and rates all run on that engine. Integration techniques are the toolbox — substitution, parts, trig methods, and partial fractions each undo a different way a function was built. Applications of integration spend those tools: areas, volumes of revolution, arc length, and average value all slice-and-sum. Sequences & series make "infinitely many terms" precise — convergence tests decide, and Taylor series rebuild functions as infinite polynomials. Parametric, polar, and differential equations reuse the same calculus in new coordinates and turn it toward modeling change over time. The toolbox for evaluating integrals. Each technique reverses a rule of differentiation: substitution undoes the chain rule, and integration by parts undoes the product rule. Trig identities and trig substitution tame roots and powers of sine and cosine. Partial fractions split a rational function into simple pieces you can integrate. When no exact antiderivative exists, numerical methods approximate the value. Topic Applications of Integration Where integration does work. Every application is the same move — slice the region into thin pieces, write one piece's contribution, then let the integral add them all up .

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