Integration

Further Mathematics S.S.S 3 First Term

WEEK 3

Integration

Performance Objectives

Students should be able to:

1. See integration as reverse process of differentiation
2. Integrate algebraic polynomial
3. Integrate logarithmic functions

Content

Properties of Definite Integral

We have so far interpreted the integral, ,  as the area bounded by the curve y = f(x), the ordinates corresponding to x = a, x = b and the x- axis.

 We now examine some properties of the definite integral

 

A₁ = ,  

A₂ = ,  

If A = abfxdx,

Then A = A₁ + A₂

Hence ,  = ,  + ,

(b) If the area is below the x – axis, it will have…