Finding area under curves by integration

 

The area under a curve and the x-axis can be found by integrating the curve between two chosen values of x.

Area = ∫ x²/4 dx

E.g.
Area under the curve between x = 1 and x = 4 = ∫ x²/4 dx
= [x³/12] ⁴₁
= 64/12 - 1/12
= 63/12
= 5.3(1 d.p.)

For interactive practice of the above, here is the applet:

For a more comprehensive tutorial on integration, including interactive practice, please follow the link: