integration

Question

How to understand integration. Would you be so kind as to give me a few examples. And explaining how to do it.

Answer 1

Integration means combining parts so that they work together or form a whole.

In others words Integration is a way of adding slices to find the whole .

Integration is often termed as the reverse process to differentiation, and has wide applications, for example in finding areas under curves and volumes of solids .

Integration can be used various applications .

(1)Integration to find the area of bounded regions .

example 

To find the area of the region bounded by the the function f(x) = cos x ,the x-axis between  x = π/4 and x = π

Answer

The area of the region bounded by the the function f(x) = cos x ,the x-axis,

and the vertical lines x = a and x = b :   

The function f(x) = cos x and vertical lines x = π/4 and x = π

      = 0.7071

Area of the region bounded by the the function f(x) = cos x and  x-axis is  0.7071 .

Answer 2

(2) Integration as reverse of differentiation .

example 

derivative of x²  is 2x .          [ derivative of  xⁿ = n x^n-1  ]

Integration of 2x is 2*x²/2 = x²        [ Integration of  xⁿ = xⁿ⁺¹/n+1]