#### Abstract

The section contains introductory questions about the indefinite integrals. The relation between integrals and derivatives will be considered. The reverse procedure of differentiation of functions will be discussed. The definition of the indefinite integral will be formulated. The section contains examples with geometric interpretation of antiderivatives. The section ends with exercises and their solutions.

#### Aim

To learn the relationship between indefinite integrals and derivatives of elementary functions. To interpret the family of antiderivatives geometrically the last part.

#### Learning outcomes

- Calculate simple integrals of elementary functions
- Apply the rules for calculating definite integrals
- Use initial conditions to determine an integral
- Calculate the area of plane regions enclosed by curves
- Apply integration to find volumes of solids
- Apply integration to solve tasks from different maritime and business applications

#### Previous knowledge of mathematics

*properties of elementary functions; graphs of elementary functions, algebra and trigonometry knowledge; rules of differentiation*

#### Relatedness with solving problems in the maritime field

Computations of indefinite integrals are used as a methodology in calculation of definite integrals. Differentiation and integration are widely used to solve many engineering problems. Practical application of integrals is part of navigation theory; for instance, integrals are used in designing the Mercator map. Derivatives and integrals helped to improve understanding of the concept of Earth’s curve: the distance ships had to travel around a curve to get to a specific location. Calculus has been used in shipbuilding for many years to determine both the curve of the ship’s hull, as well as the area under the hull.