Definite Integral

Objectives
To enable students to,
 * 1) understand the process of anti-differentiation.;
 * 2) recognize the problem of calculating areas bounded by non-linear function;
 * 3) understand how the limit of the sum of rectangles may be used to calculate the area bounded by a function;
 * 4) understand the meaning of $$\textstyle \int\limits_{a}^{b} \displaystyle f(x)dx$$;
 * 5) calculate the area under a function between two extremes;
 * 6) apply knowledge and skills relating to anti-differentiation to solve problems;
 * 7) verify that the area bounded by the curve y=f(x), x=a, x=b and x-axis =$$\textstyle \int\limits_{a}^{b} \displaystyle f(x)dx$$

Prerequisites/Instructions, prior preparations, if any
Knowledge on plotting graphs, differentiation, mapping and computing functions.

Geogebra Resources

 * File:Geometrical interpretation of definite integral.ggb


 * File:Property of definite integrals.ggb

Evaluation
Evaluate following Definite integrals and give their geometrical interpretation:
 * 1) $\int\limits_{2}^{5} (x + 1) dx$ 
 * 2) $\int\limits_{2}^{3} x dx$
 * 3) $\int\limits_{1}^{4} (x^2 - x) dx$