Application Of Integrals


Calculus has two major branches one is differential and the other is integral. Here we will discuss integral calculus it is the inverse of differentiation (process to find out the differential). There are two types of integral definite integral and indefinite integral or we can say integral is the study of these two related concepts. The indefinite integral is also known as antiderivative whereas the definite integral when calculated concludes the perfect numerical term. Integration has the shape of elongated s (∫). The main principles of the integrals were formulated in the late 17th century by Isaac Newton and Gottfried Leibniz.

It has now become an important tool in calculus which has number of application of integration in the field of science and engineering. Few of the applications of integrals are shown below:


  • The integrals can be used to determine the function of average value.

The average value function of f (x) over the interval [a, b] is

favg = 1 / (b - a) ∫ab f(x) dx.

  • These are also used in calculation of area. If we want to determine the area between two curves then we can use integrals.
  • Integrals in conic sections can be used to find the volume of solid of revolutions

The area and volume formula is V = ∫ab A (x) dx and V = ∫ab A (y) dy: where A (x) and A (y) is the area of cross – sectional area of solid.

  • Method of cylinder is also helpful in determining the volume of solids of revolutions.
  • Another application of integral is determination of amount of work which is required to move the objects.

The force required for moving an object from y = a to y = b is given by: W = ∫ab F (y) dy.

  • We can also use integration to find the centroid of an object.
  • Average value of the curve can be calculated with the help of integration. Here the head injury criterion is an application which is used in road safety research.
  • We can even use integration to calculate liquid pressure.

These all are application of integrals.

Math Topics