Integral with variable upper limit of integration Let f ( x) be a continuous function, given in a segment [ a , b ], then for any x [ a , b ] the function exists. This function is given as an integral with variable upper limit of integration in the right-hand part of the equality. All rules and properties of a definite integral apply to an integral with … [Read more...]

## Some definite integrals

Some definite integrals Back … [Read more...]

## Geometrical and mechanical applications of definite integral

Geometrical and mechanical applications of definite integral Volume of revolution body. Work of variable force. A definite integral has numerous applications in mathematics, mechanics, physics, astronomy, engineering and other fields of human activities. We’ll consider here only two examples, illustrating possibilities of this apparatus. A volume of revolution … [Read more...]

## Basic properties of definite integral

Basic properties of definite integral Back … [Read more...]

## Definite integral. Newton – Leibniz formula

Definite integral. Newton – Leibniz formula Curvilinear trapezoid. Area of a curvilinear trapezoid. Definite integral. Limits of integration. Integrand. Newton-Leibniz formula. Consider a continuous function y = f ( x ), given on a segment [a, b] and saving its sign on this segment ( Fig.8 ). The figure, bounded by a graph of this function, a segment [a, b] and … [Read more...]