CALCULUS I - INTEGRATION FULL COURSE

This course introduces the fundamental concepts and techniques of integral calculus. Students will learn how to compute definite and indefinite integrals, apply integration methods such as substitution, integration by parts, and numerical approximation (e.g., Simpson’s Rule), and use integrals to solve problems involving areas, volumes, arc lengths, and applications in physics and engineering. Emphasis is placed on developing problem-solving skills and a solid conceptual understanding of how integration complements differentiation. Keywords: integral, integration, antiderivative, indefinite integral, definite integral, Riemann sum, limit of a sum, area under a curve, fundamental theorem of calculus, u-substitution, substitution method, integration by parts, integration by partial fractions, integration by trigonometric substitution, improper integral, convergence, divergence, integrand, limits of integration, constant of integration, differential, dx, accumulation function, net area, total area, average value, mean value theorem for integrals, integration techniques, even function, odd function, symmetric interval, step function, piecewise function, integral bounds, discontinuity, singularity, improper limits, comparison test, absolute convergence, vertical asymptote, infinite interval, unit step function, delta function, shell method, washer method, disk method, volumes of revolution, arc length, surface area of revolution, integral test for convergence, numerical integration, trapezoidal rule, Simpson’s rule. TIMESTAMPS: 00:00:00 INTRO AND DEFINITION OF AN INTEGRAL 00:12:26 INTEGRATION BY CHANGE OF VARIABLES 00:33:46 INTEGRATION BY PARTS 00:44:02 VOLUME INTEGRAL CALCULATION - DISK / WASHER METHOD 00:57:06 VOLUME INTEGRAL CALCULATION - SHELL METHOD 01:14:30 NUMERICAL METHODS - RECTANGULAR 01:22:55 NUMERICAL METHODS - TRAPEZOIDAL 01:26:48 NUMERICAL METHODS - MIDPOINT 01:30:28 NUMERICAL METHODS - SIMPSON 02:36:01 IMPROPER INTEGRALS