In the preceding chapter we studied differential calculus. Now shall study Integral calculus. Integral or to integrate has two meaning. First the literal meaning is “to combine (one thing) with another to form a whole” or simply to indicate whole or sum or total of. Integral calculus exhibits this feature when we find areas bounded by curves, volume of various solids, length of curves etc. The second meaning of integrate is to find the function whose derivative is given. For example the Integral calculus helps us to find the “function” itself when rate of change is available. For example, if the formula for rate of change (velocity) is given, we can use integral calculus to produce correlation between distance travelled and time. First we will study this type of integration.  However, note that these two types of integration are closely connected.

Modern science and engineering use calculus extensively. It is biggest tool available in mathematics in exact thinking.          

Calculus is present almost all round us. It is present everywhere. It is present in Engineering, Science and Technology, Medicine, Business, Music, Meteorology. There is hardly any area where its application is not there.