What are the Applications of differentiation and integration?

Answer 1

Shipwrecks occured because the ship was not where the captain thought it should be. There was not a good enough understanding of how the Earth, stars and planets moved with respect to each other.

Calculus (differentiation and integration) was developed to improve this understanding.

Differentiation and integration can help us solve many types of real-world problems.

We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).

Derivatives are met in many engineering and science problems, especially when modelling the behaviour of moving objects.

INTEGRATION:

1. Applications of the Indefinite Integral shows how to find displacement (from velocity) and velocity (from acceleration) using the indefinite integral. There are also some electronics applications.

In primary school, we learned how to find areas of shapes with straight sides (e.g. area of a triangle or rectangle). But how do you find areas when the sides are curved? e.g.

2. Area Under a Curve and
3. Area Between 2 Curves . Answer is by Integration.

4. Volume of Solid of Revolution explains how to use integration to find the volume of an object with curved sides, e.g. wine barrels.

5. Centroid of an Area means the centre of mass. We see how to use integration to find the centroid of an area with curved sides.

6. Moments of Inertia explains how to find the resistance of a rotating body. We use integration when the shape has curved sides.

7. Work by a Variable Force shows how to find the work done on an object when the force is not constant.

8. Electric Charges have a force between them that varies depending on the amount of charge and the distance between the charges. We use integration to calculate the work done when charges are separated.

9. Average Value of a curve can be calculated using integration.