Overview

Integral calculus is easy. You don't believe that? Then let us convince you. Success in integral calculus requires the following: (1) Basic calculation skills, such as arithmetic rules and some differential calculus (derivative rules); (2) Overview of integration methods: substitution, partial integration, basic function integration, and a few tricks; (3) A practiced eye for when which method leads to the goal; and (4) The skill to apply these methods successfully. The books on integral calculus in this series support you in areas (2) through (4) by, among other things, providing over 100 examples with worked out solutions and embedded randomized digital exercises for almost infinite training opportunities. The goal of an integral calculation is always to transform the given integral into an integral whose solution you know, because the solution can be taken from a table with the so-called basic integrals. Therefore, it needs a trained eye to look at an integral and to decide which transformation, i.e. which integration method, leads to the goal. This is practiced in detail in this book. In addition, a total of 11 video tutorials are embedded at important milestones: Here topics covered in the book are explained by the author through a video. Further, the author will give you a video introduction to each chapter, if you like. All you need to do is follow the provided link or QR code. In this first volume on integral calculus, the basic integrals and calculation rules for integrals are introduced, since both must be used in any integral calculation. Subsequently, the so-called elementary substitutions are treated. These include linear and logarithmic substitution and some variants of them. You will see that the principle and procedure of substitution can be explained in a very understandable way using these elementary substitutions. Once you understand the principle, you can perform any other complex substitution, because the basic procedure is always the same. Then it is only a matter of recognizing which substitution leads to the goal. This is exactly what we practice in this book and in the subsequent volumes on integral calculus. In this volume, we also emphasize an explanation of why one writes a +C after a calculated antiderivative for indefinite integrals and why one does not do this for definite integrals. Along the way, we will understand what the dx at the end of an integral means and we will understand how to deal with integration limits after a substitution. So you will see: Integral calculus is easy!

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