A definite integral of the figure from the scalar function. Practical part: the manual for students of specialties 1-70 01 01 "Pr" is an indispensable educational resource for those who want to master the fundamental skills of working with certain integrals in the context of geometry and mathematical analysis The author’s team created this manual to help students not only understand the theoretical foundations, but also learn how to apply them in practice, which is especially important for future engineers, mathematicians and technical specialists. The book focuses on the concept of a certain integral, viewed through the prism of calculations on a figure, limited by a scalar function. This is not just a dry presentation of the theory, but a lively and fascinating immersion into the world of integrated computing, where each chapter is filled with practical tasks illustrating real-life situations and problems in the field of engineering, physics and applied mathematics. The author’s team, which includes experienced teachers and practitioners, seeks to show how theoretical knowledge turns into a powerful tool for solving complex problems. The book is intended for students enrolled in specialty 01. 01 "Software engineering" and related areas, where the skills of working with certain integrals is mandatory. It is ideal for students who are looking for a practical guide to solidify knowledge, prepare for exams, or complete coursework and thesis. It may also be of interest to teachers who are looking for modern and understandable material for their classes, as well as specialists who want to refresh or deepen their knowledge in the field of integral calculus. What makes this book especially valuable is its focus on the practical side of the issue. It examines in detail the methods of calculating certain integrals by figure, examines the features of working with various types of functions and boundaries, and gives examples from real life where this knowledge finds its application. The author's style is distinguished by clarity, logical consistency and accessibility, which allows even beginner students to easily learn complex concepts and move to independent solutions. The topics raised in the book go beyond simple calculation. Here we consider the issues of geometric interpretation, the properties of integrals, their relationship with areas and volumes, as well as methods of approximate and analytical calculation .. Particular attention is paid to practical aspects - from plotting to solving problems to calculate the area of the figure, limited by the scalar function. This makes the book not only a textbook, but also a reliable assistant in preparing for practical exams and test papers. The author's team, known for his other works in the field of mathematical analysis and applied disciplines, created a book taking into account modern training requirements. Their style is characterized by vivid presentation, logical structure and a rich set of illustrations and examples, which contributes to a deeper understanding of the material. This book is a logical continuation of classical textbooks on mathematical analysis, supplemented by practical tasks and modern approaches to solving problems. If you are looking for a tool that will help you not only understand the theory, but also teach you how to apply it in practice, "A certain integral in figure from scalar function. The practical part” will become your reliable satellite . It is suitable for students, teachers and specialists who want to improve their knowledge and confidently solve problems related to integral calculus. In this guide, everyone will find answers to their questions, as well as open up new horizons in the field of mathematical analysis, which makes it worthy of attention among educational materials in mathematics and applied analytics.