Write note on integration.

Explanation

The process of finding area is known as integration. For certain geometric shapes we can diectly find the are. But for irregular shapes the process of integration is used .
In order to find the area of the irregualr shaped curve by f(x) . The area can be divided into rectangular strips as shown in the figure . The area undre the curve is approximaterly equal to sum of areas of each rectangular strip .
It is given by `A~~f(a) Delta x + f (x_(1))Delta x + f (x_(2)) Delta x + f(b) Delta x` .
Where f(a) is the value of the function f(x) at x = a
`f(x_(1))` is the value of f(x) for `x = x_(1)` and so on.
As we increase the number of strips, the area evaluated becomes more accurate. If the area under the curve is divided into N strips, the area under the curve is given by
`A = sum_(n= 1)^(N) f_(n) (x_(n))Delta x_(n)`
As the number of strips goes to infinity `N to infty` the sum is given by ,
`underset(a)overset(h)int f(x) dx`
(Note : As ` N to infty, Delta x to 0` ) the integration will give the total area under the curve f(x) .