What is integration?

Integration can be viewed in many ways. The most common way to interpret an integral is to take the area under the curve you would like to integrate. For example Draw y=x, limit between 0 and 1, shade in the area, give answer - compare with area of triangle**C3 & C4 students try to split a function into equally spaced pieces along the x-axis. Draw straight lines to complete a segment between the x-axis and the function. Take a strip and approximate its area by a trapezium. Consider showing how making smaller segments improves the approximation. Introduce lim(n_to_0) of "change in x" and complete the expression by showing that dx=="smallest change in x". Now repeat for all strips and add up. Show equivalence with integral