Calculus 2 starts with the concept of integration, which is the reverse process of differentiation, and it involves finding the antiderivative or indefinite integral of a function, represented as ∫f(x)dx, and also the definite integral, which calculates the area under a curve between two points, represented as ∫[a,b]f(x)dx, where a and b are the limits of integration, and it can be calculated using the Fundamental Theorem of Calculus, which connects differentiation and integration, stating that if F(x) is an antiderivative of f(x) on the interval [a, b], then ∫[a,b]f(x)dx = F(b) – F(a); next, we learn about techniques for integration, like substitution (also called u-substitution), integration by parts (which is derived from the product rule), trigonometric substitution, and partial fractions (used for integrating rational functions); after mastering integration techniques, we move on to applications of integrals, like calculating areas between curves, finding volumes of solids of revolution using the disk, washer, and shell methods, arc length, and surface area of a solid of revolution; then, we dive into sequences and series, where a sequence is a list of numbers {a_n} following a specific rule, and a series is the sum of the terms of a sequence, represented as ∑a_n; we study convergence and divergence of sequences, the concept of limits applied to sequences (lim n→∞ a_n), as well as convergence tests for series, such as the geometric series test, the integral test, the comparison test, the limit comparison test, the alternating series test, and the ratio test; furthermore, we explore power series, which are infinite series that can represent a function as a sum of terms in the form of ∑c_n(x-a)^n, where c_n are the coefficients, x is the variable, and a is the center of the series, and we also learn about Taylor and Maclaurin series, which are power series expansions of a function around a specific point or the origin, respectively; finally, we delve into multivariable calculus, where we study functions of several variables, like f(x, y) or g(x, y, z), and we extend the concepts of limits, continuity, and partial derivatives (which are derivatives with respect to one variable while holding the other variables constant) to functions of multiple variables; we also study multiple integrals (double and triple integrals) and iterated integrals, which involve integration over regions in two or three dimensions, and we learn about vector calculus, including vector fields, line integrals, surface integrals, Green’s theorem (which relates a line integral around a simple closed curve to a double integral over the plane region it encloses), Stokes’ theorem (which generalizes Green’s theorem to surfaces in three dimensions), and the divergence theorem (which relates the flux of a vector field through a closed surface to the triple integral of the divergence of the field over the volume enclosed by the surface).