Integration

Further Mathematics S.S.S 3 First Term

WEEK 4

Integration

Performance Objectives

Students should be able to:

1. Associate the area under a curve with an integral
2. Calculate area under a curve using the definite integral
3. Apply integration to solve problems relating to displacement, velocity and acceleration
4. Find volumes of solids of revolution using integration.

Content

The Area under a Curve

Consider the curve y = f(x). We wish to determine the area bounded by the curve, the ordinates x = a and x = b and the x – axis.

Take a fixed point H on the curve such that OE = x and EH = y. take a neighboring point B such that OD = x + ∆x and DB =…